If I go to that mobility stat and plug in a bunch of other countries they almost all look the same and Sweden is no outlier. That is also true for the lack of increasing deaths which is nowhere to be seen compared to the first wave.
So either everyone is doing what Sweden does or Sweden is doing what everyone else does, depending on your perspective I suppose.
I gave one very big counter example: the US is social distancing at a rate roughly double that of Sweden and is getting worse results. It's also had multiple waves of deaths.
Canada isn't getting worse results, but is also roughly socially distancing twice as much as the Swedes.
The UK went down even further, down to -70% mobility.
Leaving the Anglosphere (what I'm most familiar with, sorry), Germany is now closer to Sweden, but was also below ~50% mobility. France was down to -84%!
And the Scandinavian countries: both Denmark and Norway was down to around -60%, and Finland was at around -50%.
All of these countries also rebounded from their social distancing "peak" much more slowly than Sweden.
At least among Western countries, I think a fair characterization is that while Swedes may have socially distanced on their own, based on mobility data, they did so less and for a shorter time.
Per the IMHE's COVID page [1], mobility has been depressed, around -30%-35% at peak, and that does line up with the peak of deaths, so there's some merit to your argument there.
What doesn't really line up is that mobility quickly rose again, up to around -25% and then -15% from base line, without a corresponding increase in cases, deaths, or hospitalizations. It dipped again, and then went back up, and is now hovering closer to -10%.
There's also been virtually no mask usage throughout the entire pandemic.
Compare this to the US [2], which fell to -50% at peak, and has never risen above -20% this entire time.
[1] https://covid19.healthdata.org/sweden
[2] https://covid19.healthdata.org/united-states-of-america