Remove uses of `any` in server and client

[eliandoran]

[meichthys]

Adding this to the Initial Release milestone. @eliandoran If this wasn't yet addressed in the existing PRs, feel free to remove it from the Milestone.

[pano9000]

I've started working on this as part of running eslint and fixing issues on each subdirectory in the server src folder
One of the rules it checks for is flagging usage of "any" as type.

#1347
#1384