Larger but overlooked companies that have a great training culture?

I'm searching for any job opportunities at larger companies that can "get you back up to speed" on required peripheral knowledge with some on-site training/mentoring, provided that you can take care of most of the core knowledge yourself. I want to look beyond FAANG, for other places that have a lower barrier of entry, but still provide a good training regimen.

I'm a software programmer who's been out of work since late 2019 and have roughly 10 YOE (though I fall usually in junior or mid-level rank).

What are some larger companies that can provide adequate training for people lagging behind? Perhaps consultancies and body shops are for me... if so, which in particular would you recommend?

I know the core knowledge of my job to be:

- Algorithms and data structures - Imperative and OO programming - Control flow - Design patterns

And peripheral knowledge:

- Front-end frameworks - Back-end frameworks - Cloud services - Testing - Automation and Deployment

I'm fairly good with a lot of the core knowledge, although with data structures and algorithms, my ability to solve problems using them are mostly limited to Leetcode easy problems. My peripheral knowledge needs a lot more work- many companies I've interviewed have rejected me for it. I know very little about most of them and rather out of date with frameworks. I need to get hired to begin with a training period on such knowledge before they expect me to be productive.

Also, I'm interested in startup or freelance opportunities. I have already been freelancing since 2011, and for smaller companies. Trying to pivot to a steady route that is also "low pressure" with the interviews.