XP does need an older version of Audacity.
The final version of Audacity that officially supported XP was Audacity 2.0.6.
The final version of Audacity that officially supported XP with SSE2 was Audacity 2.1.3
Unofficially, Windows XP SP3 with SSE2 could run Audacity versions up to and including Audacity 2.2.2 (and no later versions).
For Windows Vista / 7 / 8 / 8.1 I would recommend Audacity 2.4.2. Later versions may work, but are untested. Audacity 2.4.2 was the final (and best) version in the Audacity 2.x series.
For Windows 10 / 11, use the latest version of Audacity (Audacity 3.1.3).