Medicare is a program that solely exists for the retired who over 65 and disabled people.
Medicaid, on the other hand, is available to those who live in states that accepted federal funding via the ACA and are within a certain percentage of the federal poverty line.
Those who don't qualify for Medicaid, but are under a certain income level, have their health insurance premiums subsidized via the ACA.
If you plan on eliminating Medicaid, you'll need to acknowledge the fact that even people who earn many multiples of the federal poverty level are still eligible for subsidized health insurance due to burden of costs. If people who are not poor by federal standards need to have their health insurance costs subsidized, that means people whose income is derived from UBI-esque make-work programs will have a hard time affording health insurance if they're considered eligible for Medicaid, but it was eliminated.
This is why many proponents see UBI as an adjunct, not a replacement, for existing programs.
Similarly, I think socialized insurance programs should also fold in VA medical benefits, medicaid and other subsidized programs under a single umbrella. I'm not a fan of bureaucracy. That said, the post you replied to mentions no such thing.
20 hours a week is just my suggestion as a minimum that would allow for people to still job search if they choose to and could be averaged over a quarter or year or similar. Exceptions would be for those who would traditionally be on Medicare. Note: I think if UBI were implemented that Medicare and a lot of other programs should be replaced by it.