chore: Remove last deprecated method

[TerryHowe]

What this PR does / why we need it:

Remove the last deprecated method

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 66.66667% with 2 lines in your changes missing coverage. Please review.

Project coverage is 85.31%. Comparing base (374a1e3) to head (2555456).

Files	Patch %	Lines
cmd/oras/root/cp.go	66.66%	0 Missing and 1 partial :warning:
cmd/oras/root/manifest/push.go	66.66%	0 Missing and 1 partial :warning:

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1438      +/-   ##
==========================================
+ Coverage   85.28%   85.31%   +0.02%     
==========================================
  Files         107      106       -1     
  Lines        3800     3800              
==========================================
+ Hits         3241     3242       +1     
+ Misses        334      333       -1     
  Partials      225      225              

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[TerryHowe]

LGTM but I can see oras cp and oras manifest push still require a lot of refactoring. Thanks @TerryHowe

I'll look at those next, thanks.

[qweeah]

LGTM but I can see oras cp and oras manifest push still require a lot of refactoring. Thanks @TerryHowe

I'll look at those next, thanks.

Thanks, the main idea is to create dedicated display handler for cp and manifest push that implements a TaggedHandler like https://github.com/oras-project/oras/blob/f64964319489e88e4842d20b28428d1ffd065206/cmd/oras/internal/display/metadata/text/push.go#L41C1-L45C2