but now that Albert has acknowledged her as his child but denied her rights to the throne does that effectively bar her from using the style and title "HSH Princess Jazmin Grace"?
Officially, though that won't stop the media from calling her such-as they have with Eric Alexandre.
The only persons entitled to use HSH Princess of Monaco are Stephanie and Caroline-though Caroline prefers the higher status styling of HRH Caroline of Hanover.
Albert is title HSH the Sovereign Prince of Monaco. He is a ruler and addressed as such.
Caroline and Stephanie are heirs. Because their children were never intended to be
direct heirs, they were never titled and I doubt Stephanie's ever will be. Should Albert never have legitimate heirs and Caroline becomes his successor, her older children could be titled.
All of the children (Casiraghi, Ducret and Gottleib/Grimaldi) are styled as Prince/ss of Monaco, though they are not titled as such. Only Alexandra has a title as HRH Princess of Hanover, however, it is unrecognized and merely a styling like her parents.
Should Albert have legitimate children, they will be titled appropriately (Albert was given more titles as the heir apparent than his sisters). Because Jazmin is not a legitimate child, she is (now) recognized as a daughter of Albert's but not an heir.
Were Albert to legitimize Jazmin and/or Eric Alexandre, they would be titled thought I see the titling of the Casiraghi trio as a more likely scenario.
Short answer--she's not a Princess.
Ann