Welcome to the forum, PJ12!
Some ebike manufacturers (such as Aventon) program a brief pedal/motor lag by intent as a safety feature. If this was never the case in the past with your bike, then I suspect it might be an issue.
I‘m not an expert, but I’m thinking maybe a cadence or torque sensor issue?
The ”abruptness” of motor engagement can be a controller issue as well.
Even though you’re out of warranty, I might suggest starting by contacting the company and see if they have any ideas. If they are not responsive, have your local bike shop check it out if they service that brand.
I did have a similar issue with abrupt motor engagement on my ride home from work a couple months ago. It never recurred, so I’m not sure what that was about, and I never pursued it.