It is your decision. I don't know how long you have been in or what skills you had that would lend to your life after the army. If you want to stay in, looks like you have to take it. As far as the GI Bill, all I can say is EVERYTHING I have learned academically has been through Youtube or private lessons/schools that I paid for. The GI Bill will allow you to spend years learning the basic bullshit that Universities dish out. Any specific shit you want to master will require years of focused work/study to master on your own time regardless of whether or not you have use a GI Bill for a bachelor's degree. Also, working for the government? Is that what you really want to do? It's up to you. It's a roll of the dice with the vax. I guess it really depends on what is more important to you - your principles or your paycheck. I'm a principles first guy, but it has made my life more difficult, for sure. No Bell's Palsey, though!
I left the Army with an Honorable Discharge and not one person ever gave one shit about my service. If you are worried about what people say about whether or not you had an honorable discharge, how is that any different than being worried about what people think about you getting vaxxed? If EVERYONE simply said "NO" this whole thing would be over. Stand up for yourself and others will, too. The sergeant who processed my paperwork to leave the army told me "I thought you were all ate-up, but now I've seen the light. I told them I'd rather suck a fat man's asshole until his forehead caved in than sign up for another contract with the Army." They want you to be afraid and fall in line.
The lawyer better watch out he isn't suicided.