To be honest, we have moved to SSM for the most part and were more using Teleport for accessing RDS and other VPC-internal endpoints, so I guess a bastion host rather than jump host is probably closer to what we'll end up needing.
Tailscale definitely works a lot better from a pricing perspective and I like how they've put SSO in their premium pricing rather than enterprise, with SCIM being used for enterprise market segmentation instead.
That being said, AWS SSM to a bastion host, then using IAM auth for RDS and EKS will probably do most of what we need. Slightly more effort, but not so much more that it's a deal breaker.
I used to work at Teleport and am now at Tailscale. Both are solid products. Sad to see the Team offering disappearing but sounds like they are moving more towards large enterprise vs the small/medium startup/growth companies (while I was there we had a really healthy mid-market team but I think it's all gone now).
Take a look at Tailscale. If you are all in on AWS then using SSM is solid but if you have general access or other cloud access then Tailscale can probably help you out there.
I've also heard good things about Tailscale but I haven't personally used it