Enable strict mode in Typescript

[grahamalama]

As discussed in #2119, enabling strict mode in the Typescript compiler would reduce the chance of certain types of bugs occurring.

Running tsc --strict reports 321 errors. Trying to fix these errors in one PR would be a bit daunting. Instead, there might be a way to gradually enable strict checking on a per file/directory basis. There doesn't seem to be a Typescript-official way to do this, but this package looks like it could be helpful.

[grahamalama]

Another option to bring the codebase up to strict compliance would be to enable the compiler rules that comprise strict mode one at at time. Those are:

strictNullChecks
strictBindCallApply
strictFunctionTypes
strictPropertyInitialization
noImplicitAny
noImplicitThis
useUnknownInCatchVariables

[leplatrem]

That's a good idea! Let's start a branch and use this list as checkboxes. I'm willing to help!

[grahamalama]

Typescript strict mode flags applied:

• strictNullChecks
• strictBindCallApply
• strictFunctionTypes
• strictPropertyInitialization
• noImplicitAny
• noImplicitThis
• useUnknownInCatchVariables