[NTPShortcuts] Migrate from using UseMostVisitedTiles to ShortcutsType pref

Currently, New Tab page supports two shortcuts: MostVisitedSites and
CustomLinks. On desktop, user selection is stored in a boolean pref and
the logic for the shortcuts relies on the assumption that there are only
two shortcut types.

Since we plan to add a third managed shortcuts view, this migration
increases flexibility for customizing shortcuts by storing user
input in an integer preference. For the new preference, we use
the following mapping:
- 0 = TopSites
- 1 = CustomLinks
- 2 = EnterpriseShortcuts (to be added in a future CL)

To minimize impact on android and link mixing, MostVisitedSites will
store a boolean for each allowed shortcut type (custom link and enterprise
shortcuts in a later CL) which allows platforms to decide which
shortcut types to allow.

This change does the following:
- Renames the DeletedTileType to TileType for enum mapping
- Adds migration code to migrate NtpUseMostVisitedTiles to
NtpShortcutsType
- Updates the MostVisitedSites service and handler,
CustomizeChromePage handler, and New Tab Page handler

TODOs have been added to update TS and mojom files with the new enum.

Bug: b:438302330
Change-Id: I8f3c79f1135ae65ddedbcfd81fbe689d055abf12
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6871359
Commit-Queue: Alex Chen <alexwchen@chromium.org>
Reviewed-by: Tibor Goldschwendt <tiborg@chromium.org>
Reviewed-by: Avi Drissman <avi@chromium.org>
Reviewed-by: Samuel Huang <huangs@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1507114}