Yeah this isn't solved, same laggy typing issue started for me after the last update. Apple, here's the details:
iPhone 11 Pro 512GB
Software version 14.0.1
381GB HD space available
Minimal apps installed, no new apps installed recently
Symptoms: When starting to type a message, the first 2-4 letters appear, everything freezes for 2-3 seconds, then text resumes displaying. If I type "blind" while it's locked up, that typing will appear after 2-3 seconds once it unfreezes. This occurs intermittently, usually when switching to a new message. I've backed up / wiped my phone / reinstalled - same issue. It occurs in the Messages app w/ iMessage (blue) and SMS (green) messages. There's no noticeable lag on other apps so far. Battery health is great - it's the newest iPhone and it's less than a year old.
Please help because this is a constant source of irritation. You guys are great, thanks in advance.