This year, I’m planning on taking the PSAT in October and the new SAT sometime in the spring. Would a PSAT prep course sufficiently prepare me for both tests (as they are now even more similar), or should I take an SAT prep course as well/instead?
SAT prep should prepare you for PSAT, but PSAT prep by itself might not be rigorous enough for the SAT/ACT. If you did very well on the PSAT as a sophomore and wish to up your chances for NMSF, take the PSAT prep now or at least spend some time familiarizing yourself with the new format, take some practice tests, etc.
A PSAT prep course will not include anything about the essay and that is very different on the new SAT. If the SAT prep course you are considering teaches the new SAT format then just take that now and prep for the PSAT and SAT at the same time.