Show cached best_sent_depth clock analysis information also in the ANALYSIS tab #442

Description
Picochess uses the best_sent_depth optimization to prevent newly restarted shallow analysis from immediately overwriting deeper and still-useful analysis already shown on the physical clock.
This is especially visible in Mode.KIBITZ and Mode.ANALYSIS. When an entered move matches a move in the preceding Tutor or engine analysis, Picochess can reuse the known continuation, evaluation, and depth on the clock. Meanwhile, the Tutor or selected engine starts analysing the new position from a lower depth.
Consequently, the physical clock might show a deeper result while the ANALYSIS tab displays a lower-depth, growing T or E line. This behavior is intentional, but it can appear inconsistent.

Proposed improvement
Optionally show the cached clock analysis in the first row of the ANALYSIS tab, alongside the current Pico source and depth.
For example:
Pico T d7 cached: Nf6 +0.32 d20
The normal analysis line should continue showing the live search from the current position.

Suggested behavior
Show cached information only when the entered move matched an analysed continuation.
Include the cached best continuation move, evaluation, and depth.
Show it only while the live analysis depth is below the cached depth.
Hide it when the live analysis catches up.
Clear it after a deviation from the analysed lines and through the existing best_sent_depth reset paths.
Label it clearly as cached or known so it is not confused with the live analysis.
Preserve the existing clock optimization and independent, ungated web-analysis stream.
Do not change Tutor calculations, CPU usage, or WATCHER evaluations.

Value
The primary benefit is explanatory: it makes clear why the physical clock can temporarily show deeper analysis than the current T or E line in the ANALYSIS tab.
This is a low-priority display improvement. The existing behavior is correct even without it.