`Paste` on a folder's icon doesn't work

## Description



`Paste` on a folder's icon doesn't work.

## Reproduce



1. Open Jupyter Notebook.
2. Create a file, `f`.
3. Create a directory, `d`.
4. Open `f`'s context menu.
5. Click `Cut`.
6. Open `d`'s context menu.
7. Click `Paste`.
8. Expected: `f` is moved to `d` on the disk, 
9. Actual: nothing happens.
10. Expected: `f` disappears in the UI, `d` has `f` inside.
11. Actual: nothing happens.
12. Reload the page.
13. Expected: there is _no_ `f`.
14. Actual: there _is_ `f`.



## Expected behavior



`f` is moved to `d` on the disk, the UI reflects it.

## Context



- Operating System and version:  Calculate Linux (Gentoo-like).
- Browser and version:  Chromium  149.0.7827.155.

- Jupyter Notebook version:  7.6.0.



<details><summary>Troubleshoot Output</summary>
<pre>
which: no jupyter in (/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/opt/bin:/usr/lib/llvm/21/bin)
$PATH:
	/usr/local/sbin
	/usr/local/bin
	/usr/sbin
	/usr/bin
	/sbin
	/bin
	/opt/bin
	/usr/lib/llvm/21/bin

sys.path:
	/home/sasha/jupyter_issue/bin
	/usr/lib/python314.zip
	/usr/lib/python3.14
	/usr/lib/python3.14/lib-dynload
	/home/sasha/jupyter_issue/lib/python3.14/site-packages

sys.executable:
	/home/sasha/jupyter_issue/bin/python

sys.version:
	3.14.6 (main, Jun 18 2026, 07:07:18) [GCC 15.2.1 20260214]

platform.platform():
	Linux-6.18.33-calculate-x86_64-Intel-R-_Core-TM-_i5-7200U_CPU_@_2.50GHz-with-glibc2.43

pip list:
	Package                   Version
	------------------------- -----------
	anyio                     4.14.1
	argon2-cffi               25.1.0
	argon2-cffi-bindings      25.1.0
	arrow                     1.4.0
	asttokens                 3.0.1
	async-lru                 2.3.0
	attrs                     26.1.0
	babel                     2.18.0
	beautifulsoup4            4.15.0
	bleach                    6.4.0
	certifi                   2026.6.17
	cffi                      2.0.0
	charset-normalizer        3.4.7
	comm                      0.2.3
	debugpy                   1.8.21
	decorator                 5.3.1
	defusedxml                0.7.1
	executing                 2.2.1
	fastjsonschema            2.21.2
	fqdn                      1.5.1
	h11                       0.16.0
	httpcore                  1.0.9
	httpx                     0.28.1
	idna                      3.18
	ipykernel                 7.3.0
	ipython                   9.15.0
	ipython_pygments_lexers   1.1.1
	ipywidgets                8.1.8
	isoduration               20.11.0
	jedi                      0.20.0
	Jinja2                    3.1.6
	json5                     0.15.0
	jsonpointer               3.1.1
	jsonschema                4.26.0
	jsonschema-specifications 2025.9.1
	jupyter                   1.1.1
	jupyter_builder           1.0.2
	jupyter_client            8.9.1
	jupyter-console           6.6.3
	jupyter_core              5.9.1
	jupyter-events            0.12.1
	jupyter-lsp               2.3.1
	jupyter_server            2.20.0
	jupyter_server_terminals  0.5.4
	jupyterlab                4.6.0
	jupyterlab_pygments       0.3.0
	jupyterlab_server         2.28.0
	jupyterlab_widgets        3.0.16
	lark                      1.3.1
	MarkupSafe                3.0.3
	matplotlib-inline         0.2.2
	mistune                   3.3.2
	nbclient                  0.11.0
	nbconvert                 7.17.1
	nbformat                  5.10.4
	nest-asyncio2             1.7.2
	notebook                  7.6.0
	notebook_shim             0.2.4
	packaging                 26.2
	pandocfilters             1.5.1
	parso                     0.8.7
	pexpect                   4.9.0
	pip                       26.1.2
	platformdirs              4.10.0
	prometheus_client         0.25.0
	prompt_toolkit            3.0.52
	psutil                    7.2.2
	ptyprocess                0.7.0
	pure_eval                 0.2.3
	pycparser                 3.0
	Pygments                  2.20.0
	python-dateutil           2.9.0.post0
	python-json-logger        4.1.0
	PyYAML                    6.0.3
	pyzmq                     27.1.0
	referencing               0.37.0
	requests                  2.34.2
	rfc3339-validator         0.1.4
	rfc3986-validator         0.1.1
	rfc3987-syntax            1.1.0
	rpds-py                   2026.5.1
	Send2Trash                2.1.0
	setuptools                82.0.1
	six                       1.17.0
	soupsieve                 2.8.4
	stack-data                0.6.3
	terminado                 0.18.1
	tinycss2                  1.5.1
	tornado                   6.5.7
	traitlets                 5.15.1
	typing_extensions         4.15.0
	tzdata                    2026.2
	uri-template              1.3.0
	urllib3                   2.7.0
	wcwidth                   0.8.1
	webcolors                 25.10.0
	webencodings              0.5.1
	websocket-client          1.9.0
	wheel                     0.47.0
	widgetsnbextension        4.0.15
</pre>
</details>

<details><summary>Command Line Output</summary>
<pre>
[D 2026-06-28 16:08:47.549 ServerApp] Accepting token-authenticated request from 127.0.0.1
[D 2026-06-28 16:08:47.551 ServerApp] 200 GET /api/kernels?1782652127538 (d4118fbff3044f138ad1097d58a89599@127.0.0.1) 3.37ms
[D 2026-06-28 16:08:47.558 ServerApp] Accepting token-authenticated request from 127.0.0.1
[D 2026-06-28 16:08:47.560 TerminalsExtensionApp] 200 GET /api/terminals?1782652127540 (d4118fbff3044f138ad1097d58a89599@127.0.0.1) 6.06ms
[D 2026-06-28 16:08:47.561 ServerApp] Accepting token-authenticated request from 127.0.0.1
[D 2026-06-28 16:08:47.564 ServerApp] 200 GET /api/sessions?1782652127543 (d4118fbff3044f138ad1097d58a89599@127.0.0.1) 8.07ms
[D 2026-06-28 16:08:48.151 ServerApp] Accepting token-authenticated request from 127.0.0.1
[D 2026-06-28 16:08:48.197 ServerApp] 200 GET /api/contents?content=1&hash=0&1782652128141 (d4118fbff3044f138ad1097d58a89599@127.0.0.1) 46.94ms
[D 2026-06-28 16:08:57.572 ServerApp] Accepting token-authenticated request from 127.0.0.1
[D 2026-06-28 16:08:57.573 ServerApp] 200 GET /api/kernels?1782652137562 (d4118fbff3044f138ad1097d58a89599@127.0.0.1) 1.98ms
[D 2026-06-28 16:08:57.577 ServerApp] Accepting token-authenticated request from 127.0.0.1
[D 2026-06-28 16:08:57.578 TerminalsExtensionApp] 200 GET /api/terminals?1782652137573 (d4118fbff3044f138ad1097d58a89599@127.0.0.1) 1.16ms
[D 2026-06-28 16:08:57.583 ServerApp] Accepting token-authenticated request from 127.0.0.1
[D 2026-06-28 16:08:57.584 ServerApp] 200 GET /api/sessions?1782652137577 (d4118fbff3044f138ad1097d58a89599@127.0.0.1) 0.99ms
[D 2026-06-28 16:08:58.219 ServerApp] Accepting token-authenticated request from 127.0.0.1
[D 2026-06-28 16:08:58.255 ServerApp] 200 GET /api/contents?content=1&hash=0&1782652138210 (d4118fbff3044f138ad1097d58a89599@127.0.0.1) 36.92ms
[D 2026-06-28 16:08:59.181 ServerApp] Accepting token-authenticated request from 127.0.0.1
[D 2026-06-28 16:08:59.183 ServerApp] 200 PATCH /api/contents/file.txt?1782652139177 (d4118fbff3044f138ad1097d58a89599@127.0.0.1) 2.76ms
[D 2026-06-28 16:08:59.193 ServerApp] Accepting token-authenticated request from 127.0.0.1
[D 2026-06-28 16:08:59.207 ServerApp] 200 GET /api/contents?content=1&hash=0&1782652139190 (d4118fbff3044f138ad1097d58a89599@127.0.0.1) 14.17ms
</pre>
</details>

<details><summary>Browser Output</summary>

<pre>
</pre>
</details>

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`Paste` on a folder's icon doesn't work #7970

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`Paste` on a folder's icon doesn't work #7970