Of course it's worth noting that the bond market has massively sold off since inflation hit. The counterpoint is that it's arguably just going back to the mean, but nonetheless, it's a fairly historic move.
US yields at the long end (the part of the curve that is sensitive to long-term stagflation and inflation) don't necessarily indicate that participants believe that the spending isn't a problem either. Once yield started to rise, the U.S. massively twisted issuance back to T-Bills, which are short duration and essentially risk-free. Fragility on the long end is being carefully managed.
To some extent, you are seeing some financial repression, ie the shape of the yield curve is being actively managed. This expectation is built into the bond prices as well. If the long end starts to break down, nobody expects the treasury to start issuing even more long bonds. They naturally would expect them to pull back and start issuing more T-Bills and only term out the debt once the market/liquidity can handle it. There is some conversation right now about leverage limits in the banking system/SLR being expanded, so there is more capacity to warehouse the debt on the banking side. That's pushing in the direction of financial repression (where the banks are "incentivized" to shape the curve in a desired way).
0% interest rates were leveraged against the Fed Put, and it's arguable that there is a Treasury Issuance Put that is currently baked in.
I think that the issue is broader than this though. It's about much more than just the inflationary effects of spending. It's an ideological battle as well. As for bonds, there's also the fact that US bonds are a "there is no alternative" asset to some degree. Remember that bond investors got their faces ripped off in the initial rate hike cycle. There's a good parallel to commodity futures prices here, in that prices of commodity futures are terrible indicators of the actual price in the future. There is a distinction between where a market clears and a bet on future prices. It is a somewhat subtle distinction, but it is grossly underappreciated. That said, of course you can isolate the inflation expectation aspect of the bond market and you are probably correct that this indicator does not red flag inflation driven by excess spending. Of course, growth expectations are also fairly healthy. So it's hard to say what it would look like if inflation expectations stayed high and growth expectations started to fall. Then the bond market might look quite a bit different. We haven't seen a true stagflationary market in 50 years.