Fired for drinking on the job [WI]

I’ve looked at other posts on this topic and they aren’t exactly the same so I’ll give my details in the hopes I’ll get more relevant feedback.

I am an alcoholic in recovery, but recently relapsed due to family issues and the stress of the job, and was very recently caught drinking on the job and subsequently fired. I was on the job for about a year. My previous job I was laid off in April 2024. I am starting the job search and was wondering whether I include the most recent job on both my resume and on LinkedIn. I am considering saying I have been on a sabbatical since April 2024 and leaving it off. It was a job similar to all the ones I’ve had in my 25 year career, so it would show good experience if I left it on my resume and LI.

I obviously wouldn’t bring up why I left the latest job in interviews, but I am curious whether it may come up in some way in my previous employment checks that HR often does. I know when asked, much of the time companies will only disclose the role and period of time I worked there, but I also read they may ask if I am “rehireable” or something like that. How frequently is that asked by HR when they are checking previous employment? Am I better off just leaving it off or will the period of time in between (15 months) my last job and my job application too much of a red flag?

I am doubling down in my AA program and more determined than ever, so please leave that advice out of any feedback.

Thanks in advance for any feedback.