This legit looks like an IOS 15 issue. I am in the same boat, have 2.5 GB of messages. Also, I can attest because i did this thing you are asking for, 4 months ago on 14.7.1 and it worked perfectly fine. Easily deleted about 2 GB of imessages back then.
Most baffling thing this time around, I have 1 big video file (1.8GB) in imessages that i know of ever since the last cleanup; today i deleted that by going to my chat (as suggested by the community specialist here), but nothing changed in my Icloud space, so i guess the specialist response is just as useless.
This may sound like apple's ploy into forcing you to buy Icloud+.
PS: I am an android user and have to use IOS for work. I have sworn an oath never to buy icloud storage since I already have google drive and office 365/onedrive. This little incident reaffirms my belief in not using IOS personally.