How likely am I to need to visit an embassy in person for my DTV application while in Vietnam?

The purpose of your trip to Vietnam is to apply for a DTV right ? So invest your time in doing that, rather than wanting to wander around and risk getting your application rejected

First things first, so you dont waste your money, just showing $$ coming into an account isn't enough. For all they know, you could be a drug dealer. You either need to have your own verifiable company, or be employed. I think you can be an influencer, but I'm not sure how that works. There are probably posts in the group about that subject just search. If you are a freelancer you will probably need to show some contracts/agreements, possibly some payroll statements, and tax returns. If any of that is a problem then you should look into doing soft power.

Why fear for going in person to an embassy? It normally will give you better possibilities to explain your case.

For workcation you'll need either documents of your own company or documents proving you work for any other individual or company. Just saying you work remotely but not for whom, won't work.

I believe you should stay in the jurisdiction of your embassy. But you can move freely from one village/city to another. Definitely don't go out of Vietnam

For workation they will at minimum want to see a letter from your employer allowing you to work remote. If you are self employed you need to show the business docs and provide this letter to yourself. Money going into an account randomly won't cut it.

Vietnam is broken into two parts. You apply to either Hanoi or HCMC depending on where you are in Vietnam.

Possible but unlikely. You will definitely be asked for proof of location so make sure you're in the jurisdiction covered by the particular Embassy you're going to use.