Need Perl regex which matches every a software version starting from 3.10.1.0 and all further versions numbering

Don't use a regex pattern for this.

use version qw( );

if ($version >= version->declare("3.10.1.0")) {
   ...
} else {
   ...
}

This regex should do what you want.

^(?:[4-9]|[1-9]\d+)(?:\.\d+){3}|3\.[2-9]\d(?:\.\d+){2}|3\.1[1-9](?:\.\d+){2}|3\.10\.[1-9]\d?\.\d+$

It looks for all the cases where cmd_2 should run i.e.

[1-9]x.x.x.x
[4-9].x.x.x
3.[2-9]x.x.x
3.1[1-9].x.x
3.10.[1-9]x.x
3.10.[1-9].x

Demo on regex101

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