Sear is primarily a verb meaning to burn with a hot instrument. A seer is (1) one that sees, or (2) someone who claims to have powers of foresight or who claims to see supernatural things invisible to others. Sere is primarily an adjective maning withered or dried up.
If someone says, “I am a seer; all the women in my family are seers” – should “seer(s)” be capitalized?
Not necessarily, unless if in your particular case seer is a proper noun (eg Seer might be a surname).