[v23.3.x] rpk profile changes

[vbotbuildovich]

Backport #17038 to branch v23.3.x. Note that this issue was created as a placeholder, since the original PR's commit(s) could not be automatically cherry-picked.
Here are the commands to execute:

git checkout v23.3.x
git checkout -b vbotbuildovich/backport-17038-v23.3.x-12
git cherry-pick -x 117c58a8bea4dcbee21cbf4641f03c6b7868c84d ece9c0f3e45d43122c21a13315bba8892731895f 34626165c8a29d97d7c536d749540a128a8664e7 ab3103bf0ff714b89d91d81c39564e439fb39f6b 7371a47291d348484b2af3529b3ecffde8bd34a9 0e45b2d6712abf29a0f73c0395130132a0534abd 2a6609cb18d5cde1df1c4ca4b88aa8914aaba365 35635ef27d31dbad7c6ceace152f82fdc8979f48 9d555354b5003067c34b80677e1cf58b085a1b52 9c6ec387df6613d48bca7ea1089b78ee370e118e 950125149c2c1605007df43f244d717495f5afb3 a72ad92cd5dcb122e187ec240d4c44d8f00d9d1a 94e8dc031497f4bb405fe4ac4d1212e51cd7b5d5 aaa96472d22043eedafb9ec056a9dfe411dce70d 967ccf988d4000955ed5d6175208f04476890da1 eb31bb0334528bc0d3f8a092023c5ce0ec4b3e0f

git push origin vbotbuildovich/backport-17038-v23.3.x-12
gh pr create \
  --title "[v23.3.x] `rpk profile` changes" \
  --base "v23.3.x" \
  --label "kind/backport" \
  --head "vbotbuildovich/backport-17038-v23.3.x-12" \
  --draft \
  --repo "redpanda-data/redpanda" \
  --milestone "v23.3.x-next" \
  --body "Backport of PR https://github.com/redpanda-data/redpanda/pull/17038 "

[BenPope]

Fixed by #17108