Recently, I've seen people use "the supply of stablecoins has increased = it's about to take off" as a signal.

I think it's a bit like guessing the weather by how fast ice cream melts...
Honestly, an increase in supply could be a backup, or it could just be a different shell sitting outside the market; whether ETF money flows in or not isn't necessarily directly related.
Actually, the ETF side is more like foot traffic at the entrance; whether off-market funds are willing to come in still depends on sentiment and deposit/withdrawal expectations, especially since recently some places have tightened and loosened regulations and taxes, making everyone's nerves quite sensitive.
Anyway, I try to treat "related" as a reminder, not as a conclusion, and not to jump to conclusions too quickly.