This is a reconstruction of your current layout. Notice how the main timesheet content gets squeezed to almost nothing when both side panels are open. The left panel toggle and right panel toggle use different patterns, and both compete with scrollbars.

Core idea: The left panel's calendar is really just a date picker — it doesn't need 320px of permanent space. Put it in a dropdown attached to the date header. Recent matters can go there too, or in a separate quick-switch. Activity becomes a slide-over sheet. The layout is permanently: icon rail (64px) + full-width timesheet. Zero toggles, zero competing scrollbars.
When to use: If picking a date is an occasional action (not something you do every 30 seconds). Most timesheet apps have prev/next day arrows for quick navigation, and a calendar for jumping to a specific date.

Core idea: Both side panels become overlays. The left panel slides out over the timesheet (with a scrim) when you click a "calendar" icon or the date. The right panel uses a header close button. Neither panel affects the main content width — the timesheet always has full space.
When to use: If you want to keep the current information in both panels but fix the layout pressure. Good transitional approach if a bigger IA change feels too risky.

Core idea: Each icon in the rail can open a popover. Click the Calendar icon → calendar popover. Click a new "Activity" icon → activity popover. The main content area is always 100% of the remaining width. Nothing ever splits or squeezes.
When to use: If you want maximum simplicity and are okay with secondary information being one click away. This works well for tools where the primary content (timesheet) needs all available space and secondary tools are used briefly.
Tradeoff: You can only see one popover at a time. Can't have calendar and activity open simultaneously. But is that actually needed?