[release/5.0] Use NetCorePublic-Pool pool instead of AzDO hosted pool for Browser jobs (#43589) (#43598)

The hosted pool runs into no disk space issues.

Author: akoeplinger

eng/pipelines/common/xplat-setup.yml

@@ -103,12 +103,12 @@ jobs:
     ${{ if eq(parameters.jobParameters.pool, '') }}:
       pool:
         # Public Linux Build Pool
-        ${{ if and(in(parameters.osGroup, 'Linux', 'FreeBSD'), eq(variables['System.TeamProject'], 'public')) }}:
+        ${{ if and(in(parameters.osGroup, 'Linux', 'FreeBSD', 'Browser'), eq(variables['System.TeamProject'], 'public')) }}:
           name:  NetCorePublic-Pool
           queue: BuildPool.Ubuntu.1604.Amd64.Open
 
         # Official Build Linux Pool
-        ${{ if and(in(parameters.osGroup, 'Linux', 'FreeBSD'), ne(variables['System.TeamProject'], 'public')) }}:
+        ${{ if and(in(parameters.osGroup, 'Linux', 'FreeBSD', 'Browser'), ne(variables['System.TeamProject'], 'public')) }}:
           name: NetCoreInternal-Pool
           queue: BuildPool.Ubuntu.1604.Amd64