Could continued debt management and pressure in the bond market aid in strengthening the case for scarce assets like Bitcoin over the long term? Or is this simply just a normal Treasury liquidity situation/operation that has little to no relevance to Bitcoin??
The latter. What these buybacks will do is drive up the value of the bond, which means there will be more potential buyers interested in purchasing them. Furthermore, if we recall that this government promised to buy bitcoin – albeit in ‘budget-neutral ways’ – and is spending a great deal of money on this and other things, I cannot see how this could benefit the bitcoin market.
When in doubt, just assume that it has nothing to do with Bitcoin and will have no effect, you'll generally be right in the end

In fact, this helps US dollar more and if BTC has any effect it will be because of stronger USD. Which, by the way, I think is getting weaker in the last 10 years, everything they do to keep it up doesn't last. This one also won't, after temporary boost.
Long term effect of all this? People understand it is unsustainable. But reality? People should know by now. Strangely they don't care.