`/deadline` and `/scheduled` commands ignore datepicker

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### Search first

- [x] I searched and no similar issues were found

### What Happened?

When using the `/deadline` or `/scheduled` commands in a block, the date selected in the date picker that appears is ignored when the date is selected with arrow keys + enter. When a date is selected with the keyboard, the actual value is always set to today's date. When a date is selected with the mouse, the actual chosen date is used.

Additionally, the datepicker does not close after selecting a date. It stays open, both when selecting with keyboard as well as when selecting with mouse.

Other date-type-properties do automatically close when selecting a date with a mouse, but also do not work when selecting a date with keyboard.

### Reproduce the Bug

1. Enter the `/deadline` or `/schedule` commands in a block
2. Select a date (not today) with the arrow keys on the keyboard, press enter
3. Scheduled/Deadline property appears, set to today's date, in stead of selected date in datepicker.
4. Edit the date, select date with mouse
5. Date is set, but datepicker stays open
6. Edit the date, select date with keyboard
7. Date is set but immediately reverts to old value, and datepicker stays open.

### Expected Behavior

Date picker should always fill in selected date as picked in datepicker, when using mouse or keyboard or any other input method.

### Screenshots

Today == 2026-08-03

Addition 2026-08-06: Demo of trying to select scheduled/deadline + two custom date properties with keyboard and mouse.

[https://youtu.be/7tkKo5nOBVw](https://youtu.be/7tkKo5nOBVw)

### Files

_No response_

### Browser, Desktop or Mobile Platform Information

Windows 11
Logseq 2.0.1 revision b09316a

### Additional Context

_No response_

### Are you willing to submit a PR? If you know how to fix the bug.

- [ ] I'm willing to submit a PR (Thank you!)

Start by reproducing the datepicker behavior in `/deadline` and `/scheduled` blocks using both arrow keys plus Enter and the mouse. Trace the datepicker selection and command/property update flow, then verify that the selected date is preserved for every input method and that the picker closes after selection.

Written by the indexing model from the issue text.