Learn React on your own, put React on your resume, don't claim mastery over it but a vague 'know' or 'learned'. What's to lie about? But sure, it might look better in a professional context instead of just being in the keyword soup. Add at your present place a blurb: 'worked on migrating frontend to React'. You can make this true enough by simply talking to your boss "Hey, why don't we move [our native UI/command line/custom JS] to React?" and getting a "No." If it comes up in an interview, you didn't get very far and it wasn't completed. Your lack of expertise may show up in a test of ability, but then again it may not, interviews are about both sides resolving what's true enough about the resumes and the job description/requirements into what they actually care about.
And of course if you tried making a short demo as part of the learning, you can show that to the boss/the UI team, and be able to tell more in React terms how (not) far it got, though your current boss might also say "Ok" and now you have a chance to learn it more professionally. Like, that's how a lot of us learn new things -- I wanted to learn property testing, fortunately I didn't have to ask any managers (just a legal/security workflow and pom changes signed off by another team member) to add Java's QuickTheories to my team's test code. After that I used it in a few places, did a casual lunch-and-learn demo on it for the team, used it in various other places over time. I'd put property testing on my resume if a job app needed it, and just be honest that I haven't written nearly as many property tests as unit tests. It's a mindset change to write them, too, and maybe my lack of years and years and thousands of tests would be clear to someone needing such deep expertise. Or not.