Hairline crack below window, mostly vertical with a short horizontal segment
These type of cracks are common and certainly not major. IMO the size of the crack doesn't warrant taping. I would just spackle over it with a putty knife. Smooth it flat and let it dry. Work the spackle into the crack as much as you can. This will help prevent further cracking. After drying just use a damp sponge or cloth to wipe the excess off the surface along the crack. Touch up with paint if needed.
&quot;Is there any downside to leaving the crack as is behind baseboard heater?&quot;
There is no evidence that there are any structural issues from what you describe and show in the pic. I wouldn't be concerned about the crack behind the baseboard. This appears to be strictly a cosmetic issue.