Be careful, uptimerobot actually ignores TLS errors in its free plan. You will get no notification if your certificate is expired or outright invalid.
Yep, that's a good call.
Fortunately using an email address when registering a new Let's Encrypt cert will let you get warned by LE if something happens where your cert doesn't get renewed and is about to expire.
Kubernetes probes are much different in my opinion.
Your Kubernetes liveness check will check if things are working inside of your cluster which is great for a high frequency checkup to potentially modify the state of your pod based on the result.
But Uptime Robot is an end to end test. It tests a real connection over the internet to your domain which exercises external DNS, traffic flowing through any reverse proxies, your SSL certificate, etc..
Both compliment each other for different use cases.