I would use a QR menu to browse, if it works well enough, and otherwise ask for a real menu or else just leave.
What I will not do is make accounts, or fill in an online order form. And I will not give out any personal information, including my email, without very good reason.
Last year here in Germany the government started to require restaurants to take down the name, address, phone number of every customer, so they could contact trace if there was an outbreak. Fine by me, in these special circumstances. But one restaurant we visited actually had a waiter show up with a tablet showing some online form I was supposed to fill out. I told her "No thanks, please get me a piece of paper and I will write it down". The owner then came with pen and paper, and we had a nice and friendly chat. He explained that he wanted to make it easy and "cool" with tech. It also turned out that his "tech-wiz" nephew had coded up that online form for him last minute (very cliché :p). I explained to him that while understandable, it's actually harder for a lot of people to type on these things (including me to a degree) than use a pen and paper - the owner thought for a few moments and admitted that he too finds it easier to use a real pen "at his age" - and that storing this kind of information in digital form is just one mishap away from really angry (former) customers and GDPR penalties, and how managing this kind of data is actually harder to get right in digital form than collecting some pieces of paper and running them through the shredder some 4 weeks later. We visited the same place about a month later, and they had switched to pen and paper entirely. I like to think our talk helped them with that decision.
I cannot really fault that owner. He was trying to do the best in a suddenly changed and shitty situation, and in his line of business he didn't really have to deal with privacy issues and the associated dangers and regulations before, other than cashless payments where the payment processor does most of the heavy lifting and compliance anyway.