For JS files loaded by <script>, we can support both module-aware browsers and non-module-aware browsers as below:

<script type="module" src="module_script.js"></script>
<script nomodule src="classic_script.js"></script>

Module-aware browsers load the first one, and non-module aware browsers load the second one by ignoring type="module" script and nomodule attribute.

Then, how about Link: headers and <link> tags with rel="serviceworker"?
IIUC, there is no similar trick to prevent old browsers from loading SW script link with workertype="module", or to disable classic SW on new browsers.

To achieve that, IMO, can we change rel="serviceworker" to rel="some-keyword-other-than-serviceworker-to-declare-serviceworker-module" for workertype="module", and add nomodule keyword to <link>?