Revision 2: A telepath must install a countermeasure in a guarded government facility, before an anti-telepath weapon is launched.

Why is the objective to install a safeguard and not to destroy the weapon?

The stakes are clear. You're missing the event section (why now?) but I assume it's just that the telepath finds out about the weapon somehow.

The bigger issue is, now that you can see the story at its core ... what makes this story or screenplay worth a reader's time? Because I've definitely already seen ?magic people must destroy doomsday weapon? - in Star Wars or X-Men or a dozen others. What's unique about this iteration?

Reviewing version 2 //?

As Nir Shelter pointed out there is no longer an inciting incident but you're getting closer. This needs to be how she discovered the weapon and it needs to be exciting and visual. This first scene is the audience's first introduction to your SciFi world and you need to show them around and make sure they understand it fully before the story really kicks in. If telepathy is such a strong feature, the inciting incident should use it BUT figure out a way to make this visual. Telepathy is a boring superpower onscreen because it all happens inside their heads.

"Install a countermeasure" is a very vague goal and again, it all sounds too easy. Why not "must lead a group of highly-skilled misfits and break into a high security government facility to disable the device before..." Now I can see the story. This is the bit of the logline that describes the bulk of the story so it needs to sound like there'll be obstacles to overcome.

"Anti-telepath weapon" - it's better than the whole deep emotion thing but make it more primal. Does this machine simply disable the ability to telepathically communicate? Make it a machine that will kill all the telepaths and if it is, stick it in the logline.

After overhearing a government plot to wipe out all telepaths while being tortured for her abilities, an antisocial telepath must?lead a group of skilled misfits, break into a high security facility and disable the device capable of wiping out her kind.

This is way too wordy but hopefully it gives you some ideas.

Jessie,

In future, please repost revisions under the original logline.

About the logline, agreed with the comments above. I'll add that in this new version there's no inciting incident, what was the event that sets the MC off on his or her journey?
If it's a government facility, wouldn't the weapon be developed under wraps? How did the MC find out about it?