[Playground] Merge Log and Output tabs into one and add there filtering

[damccorm]

As a Beam Playground User, I want to have one tab with Logs and Outputs so I can filter them to see just Logs, Outputs, or both.

Acceptance criteria:

• Logs and Outputs are at the same tab
• Logs and Outputs appear as they come
• Logs and Outputs can be filtered
• Logs and Outputs are showed both as default

Imported from Jira BEAM-13756. Original Jira may contain additional context.
Reported by: Artur.Khanin.

[damccorm]

Unable to assign user @miamihotline. If able, self-assign, otherwise tag @damccorm so that he can assign you. Because of GitHub's spam prevention system, your activity is required to enable assignment in this repo.

[miamihotline]

.take-issue

[miamihotline]

.close-issue