@Dreamy_Jazz are you planning to bring up these questions for checkusers to consult on?

Currently Special:CheckUserLog says that an initiator search term is not valid if it's an IP address. Should this be extended to temporary users (so temporary account usernames are considered an invalid search term)?

I would think so. Temporary users don't have real accounts and won't be able to become checkusers. It makes sense that they should not qualify as an "initiator" for a check.

I had not thought of doing so because this depends on the direction being taken with respect to user groups. Once that direction is taken, the question answers will be clear enough IMO to not require an email to checkuser-l. I will ask on the IRC (as I've had feedback that the checkuser-l emails can get a little too much).

stwalkerster has pointed out that it is technically possible for everyone (including temporary accounts) to have the ability to access Special:CheckUser/Special:Investigate using:

$wgGroupPermissions['*']['checkuser'] = true;

However, that use case may be too unlikely that it's not worth considering as being used in a production environment. This rule would mean that IPs would have the right to make checks, which Special:CheckUserLog does not support.