There is a Special:EditTags page, which should allow you to set tags manual (you have to start it from the history by checking some revisions and click the button on the right)

Yes, I mentioned it as "action=editchangetags" above

You can already do this. In your semi-automatic tool, inject into the edit form an element of the form <input type="hidden" name="wpChangeTags" value="tag 1,tag 2"> where the value is a comma-separated list of the internal change tag names. Be sure that the change tags are activated, or the edit will fail.

I'm pretty sure that is an undocumented feature, but I really have no idea where to document it...

The use case for tagging during manual editing is so minuscule that I don't think you could possibly justify cluttering the edit screen with an input field for tags.

TTO thank you for the wpChangeTags suggestion. Maybe it can be documented here: https://www.mediawiki.org/wiki/Manual:Parameters_to_index.php#Optional_additional_data ?

Changing during manual editing - I agree that usually it isn't used, but it may be "the chicken or egg paradox", and once such option exist it would be used, and it may be relevant for many cases.
Here is a theoretical question: are there very common comments? should we consider use tag instead of comment for them?
enwiki provides a gadget (other wikis too) for filling up common comments which include: Adding category/link, removing unsourced, copyedit or revert with explanations etc.
One could consider to replace them all, or partially with tags - gaining similar result for in user perspective but "structured" (vs unstructured summary) - which is more powerful as it allow coloring/filtering major changes in the article history. [this can be done with the wgChangeTags above but sometimes users add them manually]

Practical examples for use cases for manually tags - query:

Here is a practical query to validate it (some of the results are automatic edits, good candidates for tags with the API, and some are non automatic):

select rc_comment, count(*) from recentchanges  where not exists(select * from  change_tag where rc_id= ct_rc_id) and rc_comment<>'' and rc_comment not like '/*%' group by rc_comment order by count(*) desc limit 50

In T109032#1538694, @eranroz wrote:

enwiki provides a gadget (other wikis too) for filling up common comments which include: Adding category/link, removing unsourced, copyedit or revert with explanations etc.

Enwiki's gadget looks/works like this: https://commons.wikimedia.org/wiki/File:Gadget-defaultsummaries-screenshots.png (code at https://en.wikipedia.org/wiki/MediaWiki:Gadget-defaultsummaries.js )
Frwiki's gadget looks/works like this: https://commons.wikimedia.org/wiki/File:Gadget-ResumeDeluxe-screenshot.png (extensive documentation here: https://fr.wikipedia.org/wiki/Aide:Résumé_Deluxe )

It should be easy for someone to write a user script or gadget to add tag input to the web UI edit form, using the information that TTO provided at T109032#1538531.

Making this actually part of MediaWiki would similarly be technically easy, but would likely require significant Design work to figure out how to display it in a way that wouldn't be horrendously confusing or in-the-way for casual editors.

Change 282456 had a related patch set uploaded (by Eranroz):
Allow tags in summary

https://gerrit.wikimedia.org/r/282456

So why was @eranroz patch never merged? I could really use this functionality. Should I re-create the patch?

In T109032#3144319, @Sophivorus wrote:

So why was @eranroz patch never merged? I could really use this functionality. Should I re-create the patch?

Because I'd not seen it yet. Will respond now.

Technically its possible to add tags manually alongside an edit when editing manually: [1] is tagged with Huggle, WPCleaner, STiki, and AWB, and those are all tags that are applied manually by users at the time of editing - normally the application includes the tag, but I manually included all 4. The biggest issue I see is adding a good user interface to set what tags a user wants applied

[1] https://en.wikipedia.org/w/index.php?title=User:DannyS712/sandbox&diff=958359176&oldid=957618987&diffmode=source

See also https://www.mediawiki.org/wiki/Extension:StaffEdits