Switch designed to take #14 only
Back to the store it goes.
Switches which only take backstab connections are the cheapest of the builder/slumlord grade cheap.
Backstab connection, in general, are bad news - while legal, they are widely known to be unreliable.  They tend to knock out half your circuit and send you on a frustrating &quot;bug hunt&quot; - hang out here for a week and you'll see 2-3 such questions pop up.
Further, backstab connections can only be used once because pulling the wire out fatigues the spring.  I have a hunch this is a used one, and into the trash that goes!
New builder-grade switches are about 75 cents and have side screws.  New spec-grade switches are $3 and allow screw-to-clamp (2 wires under each screw; no backstab) which is safe to reuse.
No part of a 20A circuit can be #14 wire.
None.  You simply need to use appropriate hardware. That ain't it.
You do not need to use the expensive 20A-rated switches, unless the load you are switching is actually that big :)