In don’t think anyone can tell you from a photo. You need an arborist to look at it.
You can talk to the neighbor and express your concern. Ideally, have a paper trail in case something does happen.
You can have an arborist trim any branches hanging over your property without asking the neighbor.
I would get an estimate from a couple arborists for the trimming what’s over your yard. Then, approach the neighbor and offer to pay that amount towards having the whole thing trimmed—must include trimming the parts over your yard.
I wouldn’t pay until the work is done.
If you don’t know the neighbor at all and/or can’t be sure they’re trustworthy, I’d just get the part over your yard done.
You use an account but it’s virtually anonymous. You can buy a sort of prepaid card that you activate. You never have to give personal information.
That’s different than what Proton is doing which is to connect you to their free tier without any authentication.