`litedown`-rendered man pages could have pre-run examples

[aitap]

Originally posted by @Breeze-Hu in #7534 (comment)

Compared to the previous version, the functions in the example section aren't outputting their execution results. Is this intentional?

Pre-running examples is easy (see f65f7b3), but they currently fail because litedown calls round(<IDate | ITime>, digits = <numeric>) for columns where is.numeric(.) is TRUE. Changing is.numeric(<IDate | ITime>) to FALSE is also easy and doesn't seem to break anything inside data.table (see 63f1a73) but may be a breaking change for data.table's reverse dependencies.

How to proceed? Change is.numeric to FALSE, run a reverse dependency check, hopefully find out that nothing broke, fix the website?