I'm seeing this on an M1 mini with Tahoe onboard. This occurred while on Sequoia as well. The 'bloom' appears to occur both in iMessage (to the point of being frustratingly unusable) and to a lesser degree, Notes. There is mild bloom in Safari. I do not see this in the Chrome browser. So my gut here is this is relevant to macOS apps.
I have tried all of the above, night settings, restarts, safe mode, etc etc. All to no effect. One thing that did strike me however is that, if I changed the color theme (in this case to orange), while the text cursor and various button, section highlighting is orange in some macOS apps, the iMessage cursor color is still blue (the conversations however, on click, change to the theme color as specified). .
As some have mentioned, the amount of bloom varies, peculiarly with time.
Here's an example in Apple Notes (with theme 'Orange' - it really doesn't matter the color to be frank - this is workable though. I haven't seen any more pronounced bloom in Notes. ):

And here's the wonderful bloom in iMessage (and this is when it's behaving - otherwise the bloom is out of control - can't even see letters adjacent to the cursor at times):
