## Context
For unified logs, postgres connection logs are being filtered out by
default previously from this
[PR](https://github.com/supabase/supabase/pull/46371) due to its noise.
We're opting to show the connection logs by default instead so this PR
changes that behaviour + adjusts the connection logs filter UI
In particular this is timely as we're adjusting how the DB will log
connections based on this
[changelog](https://github.com/orgs/supabase/discussions/47197), and
we'd want to make sure that users can find their connection logs easily
## Changes involved
- [ ] Search parameter renamed to `show_connection_logs` so that we
don't need to flip its boolean value for the checkbox
- [ ] `show_connection_logs` is subsequently `true` by default
- [ ] Shift connection logs filter to a nested option under Postgres log
type
- Makes it more visual that connection logs are related to the Postgres
service
- Currently its hidden all the way in the bottom under "Misc" which can
be easily missed
- <img width="302" height="151" alt="image"
src="https://github.com/user-attachments/assets/e3e61ac7-aa16-4769-a89e-e911daacea27"
/>
- <img width="289" height="156" alt="image"
src="https://github.com/user-attachments/assets/c70ac7c4-d2f7-4961-a6d6-6653c59d8548"
/>
<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit
* **New Features**
* Unified Logs now supports expandable, nested “Log Type” filter options
for drilling into connection-related entries.
* **UI Improvements**
* Connection logs are visible by default; the visibility control has
been integrated into the main filter experience.
* Filter panels are now streamlined, and key filters (such as “Level”,
“Status”, and “Method”) have been reordered and adjusted for a cleaner
default state.
* **Bug Fixes**
* Updated Unified Logs query/test behavior to match the new
connection-log visibility logic.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->
Joshen Lim
772b3bb36e