Align console logging example with ASP.NET Core logging example

[reyang]

Essentially stealing good stuff from #4821.

[codecov]

Codecov Report

Merging #4855 (7ac5189) into main (fe78453) will increase coverage by 0.04%.
Report is 2 commits behind head on main.
The diff coverage is n/a.

@@            Coverage Diff             @@
##             main    #4855      +/-   ##
==========================================
+ Coverage   83.91%   83.95%   +0.04%     
==========================================
  Files         293      293              
  Lines       12028    12021       -7     
==========================================
- Hits        10093    10092       -1     
+ Misses       1935     1929       -6     

Files Changed	Coverage
src/OpenTelemetry.Shims.OpenTracing/TracerShim.cs	ø

[cijothomas]

not something introduced in this PR, but the "using" is accidentally/un-intentionally copied as-is by a lot of users into their helper methods, and the LoggerFactory ends up disposed when the helper method exits.

[reyang]

What options do we have and which one do you like?

1. Remove using, leave Dispose to GC finalizer (if there is a finalizer).
2. Add a comment to tell the user.
3. Remove using, add an explicit Dispose at the end of the application.

I'll give 1) -100, 2) +2, 3) +1

[cijothomas]

A combination of 2, 3 i.e remove using, and add explicit Dispose at the end. And comments saying

1. Loggerfactory must be kept active for the logging to work. (to warn about disposing too early)
2. Loggerfactory must be disposed at the end/shutdown to make sure any in-buffers telemetry is pushed out as well. (to warn about not disposing at all)

Not something to be fixed for this PR, as this issue is there for other getting-started docs as well