(Unsure if this is the right forum to ask this question, but here goes:)

From what I understand, IP Anycast can be used to steer traffic into a server that's close to the client.

I am curious if anyone here has/encountered a setup where they use anycast IP on their gateways... to have a predictable egress IP for their traffic, regardless of where they are located?

Stateless outbound load-balancing setups exist.

Example you have two  or more nat44 / nat64 / cgnat boxes behind a common ecmp path with the same destination IP(s).  this is normally so that you have more boxes that accumulate state rather than being bound to a single one.

For example, a search engine crawler could in principle have the same IP advertised all over the world, but it looks like they don't...  I wonder why?

So this is a somewhat different problem...

There's  no assurance that when you initiate a connection that the return path will return to the same instance of your anycast announcement  when the server on the other side  replies.

Effectively the initiating party needs a unicast address or you need some out of band path to get an errant packet back to the correct host.

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Vimal