what is my system's weakest link?

I don't think there is a consensus to change speakers.

I agree with Krell_man. I have not checked you items specs specifically, but I suspect most any Thiels will not be driven to full potential except by perhaps the very best, biggest, and powerful integrated amps out there. A 50 w/ch SS amp may sound nice, but is almost certainly not up to the task of pushing any Thiels to their max, which is what you want to do to get the best sound out of ANY speakers.

Thiels are NOT warm, for that flavor, look elsewhere. Thiel have unique
charm. When fed right. Not inherently warm at all. More clean and
detailed, especially if fed right.

Bottom line is how much do you like the THiels and want to invest in getting the most out of them. AN amp upgrade would be the initial solution.

Focal is a good option to consider. They are much easier to drive than Thiel in most cases, and I tend to think of the two as being in the same general sound quality camp when things are going well. Worth considering. Triangle (also French like Focal and also generally much easier to drive than Thiel as well) would be another.

Amp power ratings help determine how loud and clear things can go in various size rooms, but there is more to what the right power amp brings to the table sound quality-wise.

Current delivery (peak amps) is a better indicator of how well an amp will drive more difficult load speakers like Thiel even at low volumes. Driving better at low volumes generally means better tonality, detail, articulation and most other things associated with good sound, a more natural and "effortless" delivery top to bottom. A 40 watt power amp with high current delivery will sound different and likely much better, all other things aside, than one with less, in the case of the Thiels.

Source improvements may be hard to assess if the bottleneck is the amps ability to drive the speakers to their max, even at lower volumes, due to limited current delivery, as is more typical with integrated amps than separate power amps due to the physical limitations imposed by having powr amp in close proximity to line level and even lower phono level circuits.. Once amp/speaker combo is in a good place, then one is in a better position to assess how well changes in source devices work or not, and it will be much easier to make improvements with that from there.

BTW, most speaker designs that target extended bass in a smaller box (a popular choice practically for many these days) is likely to be a difficult load for an amp to drive. Thiels are just one case. They are very good speakers. Just not ones that will perform equally well with just any amp.

A decent tube pre-amp might be the ticket to a somewhat warmer sound with the Thiels. A juicier amp to go along with it to better address the rest of the goals perhaps.

Dynaudio would be one brand to consider for perhaps a tad warmer sounding option to the Thiels.

Adding a powered sub or two to the Thiels might help also, espcially if you think they may be undersized to deliver good extended bass in what sounds like a decent sized room.

Lots of ways to skin these cats. WIres might help fine tune things as well later if needed, but may not be the place to start in this case.