trouble logging into sites and getting verification codes

Is there something that changed about Safari, possibly as long ago as updating to Sonoma from Ventura, that is making websites think I am a bot or something else suspicious? Some time back, I started having a lot of trouble logging into various websites, all of which were ones I used regularly. One site in particular has specifically said "to protect our customers, we monitor for bot activities and it looks like you've hit one of our indicators." Got that msg multiple times.

Along with that (related? not related?), verification codes from websites that want me to prove I'm who I say I am aren't showing up at all. This is also happening across a range of websites and makes no sense to me.

I'm on an iMac with Sonoma and as of two days ago it was the latest version. Have done a lot of my internet access via private browsing and thought that might be part of the problem, but it's no better without using that privacy feature.

I've spoken with some of these companies and gave gone through the lobotomized "have you cleared your cache and cookies?" nonsense until I got to someone who finally told me NOT to clear them. I understand the logic behind that, but it still doesn't always work. I know these places have my correct email address because I still get promo or informational emails. About once every 20 attempts, I'll get in without having to call and talk to three different people.

Can't absolutely pinpoint it to the OS change, but it seems as if it was around that time. Currently not getting codes from our bank and various retailers, but again, get other emails from them all, so...??