Career advice: Never go "foobar-only". Make an effort to learn "foobar" but understand whatever is one layer below it in the stack. Want to go "cloud-only"? Learn OpenCloud, not AWS.
However, I would definitely learn a SQL dialect and learn how RDBMSes such as Postgres work (especially what is meant by ACID) as most companies are based around a database. Don't believe the hype - SQL is not dead. Dynamo is a great technology but there are many problems it can't solve for you.
Finally, I personally don't know Azure or GCP so well. Only knowing AWS in-depth hasn't held me back so far. I've used a few of Azure's services but I've never built a serious app on it.
My recommendation is to not really worry about individual technologies and to focus on safely handling and working with data.
I learned React and later React-Native. Selling myself as a "mobile consultant" then worked fine, nobody cared "how" I made these mobile apps.
My idea was the same with back-end, learning some framework and start selling myself as "mobile cloud consultant" or something, with the hopes that clients also don't care "how" I create these cloud back-ends.
I know SQL, worked most of my time with RDBMSs, so this wouldn't be big of an issue. As I said I already did a few back-ends, but my focus was on front-end, usability and such.
I just mentioned DynamoDB because I had the impression that it was "the AWS DB", do they offer an SQL service besides Redshift?
It allows you to launch many common database engines, which are managed and backed up by AWS. I've been using it for a few years and for my use-case it's great.
DynamoDB is noSQL database.
RDS somehow sounded like the Redis service of AWS, hehe.
I'm thinking about going full-stack next year. I have a bit of experience building APIs besides being mainly a front-end developer.
Is going "cloud only" a good idea? I thought about starting with AWS Lambda, S3, DynamoDB and the Serverless framework.
Are the providers hugely different or is it a good idea to spread out and do some Azure and GCP too?