Jael gets her props from Deborah’s song:
“Blessed above women be Jael,
The wife of Heber the Kenite,
Extolled above women in the tent.”
The point seems to be that she was extolled above women who stay in the tent, because she acted like a warrior. Not bad on the Israeli heroine scale.
Of course, Deborah also did her warleader stuff, but she didn’t extol herself, obviously!
And yes, there’s definitely a connection between the praise of Jael by Deborah and Barak, and the greeting of Elizabeth praising Mary and Jesus. You’re supposed to get that, if you’re an early Jewish or Gentile Christian steeped in the OT Scriptures. Jael and Deborah were famous; so Elizabeth was comparing herself to the older prophetess Deborah and Mary to the younger Jael. It probably gave them both courage, since both Deborah and Jael had done strange stuff for the Lord; and Elizabeth was acting as a prophetess that very moment, so she had a right to compare herself to Deborah.
You can get into all sorts of other comparisons, as Scripture commentators often have done. For example, Mary the Woman stomping the head of the serpent (by bearing Jesus and by obeying God sinlessly) just like Jael spiked the head of Sisera when the Lord delivered him into the hand of a Woman. Barak being a bit shy about acting as warleader is like Elizabeth’s husband Zechariah not believing the angel. And so on.