Is counting the Omer nowadays considered a time-bound Mitzva that women are exempt from?
R' C Cohen writes in Dose of Halacha
.. There is another machlokes as to whether women are obligated at all. Ramban (Kiddushin 34a) holds that women are obligated, while Rambam (Temidin Umusafin 7:24; Sefer Hamitzvot 161) and the Magen Avraham (OC 489:1) hold that as it is a time-bound mitzva, women are exempt.
The Mishna Berura (489:3) quotes the Shulchan Shlomo (489:3) who writes that as women will probably forget to count one night they shouldn’t count with a beracha at all. Nonetheless, the Aruch Hashulchan (OC 489:4) and R’ Ephraim Greenblatt (Rivevos Ephraim 1:327; 6:257:23) write that women do keep this mitzva nowadays and should count with a beracha. Especially as people set alarms nowadays to remind themselves of such things, women should do so, too.