Well, it's not actually whether it's filtered that determines the water change schedule, but whether it is cycled
. Since you're new to bettas, reading this article on the aquarium cycle will make everything less complicated for you:
For a cycled tank you never need to do a full clean out- usually you change 25-50% of the water weekly. However, for an uncycled tank, doing full water changes at least once per week is essential. Most people recommend one 50% and one 100% (where everything gets cleaned out really well) each week. The best way to determine if your water change schedule is sufficient is to get an ammonia test kit (which I highly advise everyone to do) and test the water just before each water change for the first several weeks. You always want ammonia to be below detectable levels, which equates to a reading of 0 ppm on your test kit.
Since your tank is new (and therefore uncycled), I would stick to the water change schedule for uncycled tanks rather than trying to cycle it. It can be difficult even for experienced fishkeepers to establish a stable cycle on a 2.5 gallon, so it will be a lot easier for both you and your fish to just stick to more frequent and larger water changes. Hope this helped. Welcome to the forum!