The synagogue of Satan refers to specific Jewish communities in Smyrna and Philadelphia that were persecuting the church, not to any modern situation.

https://www.gotquestions.org/synagogue-of-Satan.html

Those who persecuted the believers (the persecutors were religious hypocrites in this case) would one day realize Christ loves His children.

https://www.gotquestions.org/church-in-Philadelphia.html

This is not a blanket reference to all of Judaism, nor all of the Jewish people. Rather, Jesus is indicting a specific group in a specific area. In fact, Jesus said these offenders were Jews in name only. He called them liars. They actually belonged to Satan and served Him.

Jesus promised to compel the false Jews to acknowledge the believers' valid faith in Jesus and recognize that Jesus loves the believers. This is most likely a reference to the ultimate victory of good over evil: the day when all false teachers will have to bow to Jesus and confess that He is Lord (Philippians 2:19–11). Christians will witness that triumphant event (Revelation 20:12–15).

https://www.bibleref.com/Revelation/3/Revelation-3-9.html