On Anung's position (I still don't really know what it was, as neither of you have provided me the quoted post), my position continues to be that he was wrong and his reservations were counterproductive but that it's not irrational or illogical to attach conditions to government entitlements and not to market income. Later in our exchange, I believe that you clarified that you were not talking about all government entitlements (such as ones earmarked for specific expenditures by recipients) but rather cash payments meant as stimulus or supplemental income. With that clarification, I agree. However, to provide a for-instance, if the voting public were specifically worried about a single issue and were hesitant to allot entitlements for fear that they would not address that issue (housing payments, for instance), I don't think it's unreasonable to attach conditions onto those entitlements that they be spent toward that purpose just because persons derive market income that isn't conditional on any public purpose. Like I said, that's democracy. And democratic initiatives come through politics.
On your argument about "market-oriented liberals," I would agree that most self-identified liberals favor cash payouts without any stipulations. I would also forecast that self-identified progressives favor it at a higher percentage than liberals. When you see hand-wringing about frivolity and means-testing, it's coming from persons like Mark Warner, Joe Manchin, and Kyrsten Sinema....and it's being most vocally opposed by persons like Bernie Sanders, AOC, and Jamaal Bowman. Just like the ACA was kept to the strictest market conditions by centrists liberals like Mary Landrieu, Blanche Lincoln, and Joe Lieberman who opposed the public option, not progressives like Bernie Sanders who supported it and more. So it's strange to say "conservatives and progressives are worried about the poors being reckless." It's a nonsensical leftward punch that conspicuously mentions one group without mentioning another to which the criticism applies to a greater degree.
In re neoliberals/neoliberalism, it's a loaded term. If you, for instance, talk to someone from India about what "neoliberal" means, their concept is much clearer because the effects of neoliberalism (lowered trade and investment barriers, dismantling of labor union power, relaxed regulations on wages and profits, privatization of public services, sturdy presumptions against economic and industrial regulation generally) were much more tangible than in the United States. Here, where the neoliberal order didn't have impacts of the same magnitude and where "liberal" has its own rigid partisan meaning, it's more opaque. Persons on the left tend to apply it to New Democrat types that largely abandoned class politics rhetoric, are supportive of free trade policies (something I've softened on quite a bit tbh), and, yes, worry about issues of receding market logic (removing [dis]incentives from healthcare usage, removing [dis]incentives from borrowing loans [see DWS on payday loan reform in Florida], removing incentives to work by failing to properly condition welfare payments, etc.).
Anyways, can't speak to how wide-ranging the definition of "austerity" should be. I think it's typically used to describe any policy initiatives that seeks to lower public spending in a way that adversely affects the lower classes, rather than increase taxes.