[Feature] Improve the HTTP API typescript example

[Pigius]

Hi @pgrzesik, some improvements to the already existing repo.

• added proper types for lambda event handler (it's pointless to use any here).
• updated packages.

[pgrzesik]

Hey @Pigius - I don't have access to this repo anymore, you might need to request @mnapoli or @medikoo for a review here

Looks good to me thought 👍