Uses consistent error types in tiered storage

[brooksprumo]

Problem

The error types are inconsistent across tiered storage. This is not a functional issue, but I do find consistency to aid in understanding. So why not be consistent if we can?

Summary of Changes

• Use TieredStorageResult instead of TsResult
  • Since we only used the alias in one place, it was more consistent to spell it out completely
• IoResult for std io errors
  • This is a common pattern in Rust, and resolves the std::io::Result<T> vs Result<T, std::io::Error> differences

[codecov]

Codecov Report

Merging #34110 (501da6f) into master (f005075) will increase coverage by 0.0%.
Report is 23 commits behind head on master.
The diff coverage is 82.3%.

Additional details and impacted files

@@           Coverage Diff           @@
##           master   #34110   +/-   ##
=======================================
  Coverage    81.9%    81.9%           
=======================================
  Files         812      812           
  Lines      219737   219737           
=======================================
+ Hits       180028   180078   +50     
+ Misses      39709    39659   -50     

[yhchiang-sol]

Neat! Thanks for improving this!