Use common sessioner for API and web routes (#18114)

Use common sessioner for API and web routes (#18114)

* Use common sessioner for API and web routes

Since the regenerate session ID PR some users of the memory session provider have been
reporting difficulties with getting API results.

I am uncertain as to why this is happening - but I think that the sessioner being
created twice may be a potential cause for this. Therefore this PR attempts to move
this out to a common sessioner as it is in 1.16.

Fix #18070

Signed-off-by: Andrew Thornton <art27@cantab.net>
* Update routers/init.go