Thank you for reporting the bug. I can confirm that the bug is present in the versions of LibreOffice shown below. Both "OceanBlue" and "LightApplicationColor" themes were downloaded and installed

Version 25.8 below did not prompt for restart, and no changes were visible following a manual restart.

Version: 25.8.0.0.alpha0+ (X86_64) / LibreOffice Community
Build ID: 9bc5b89c149497a83117edfadc3fb0b96d2f9899
CPU threads: 2; OS: Windows 10 X86_64 (build 19045); UI render: Skia/Raster; VCL: win
Locale: en-US (en_US); UI: en-US
Calc: threaded

Version 25.2 below prompted for reboot once the new theme was applied, but no changes were visible.

Version: 25.2.3.2 (X86_64) / LibreOffice Community
Build ID: bbb074479178df812d175f709636b368952c2ce3
CPU threads: 2; OS: Windows 10 X86_64 (10.0 build 19045); UI render: Skia/Raster; VCL: win
Locale: en-US (en_US); UI: en-US
Calc: threaded

I tried test with "Office 2003 Blue" theme and linux-64-25.8.
Some items are applied without rebooting, but they don't seem to be rendered properly.

author	Michael Weghorn
commit 295fee0f78c002ca20708fdfd57d52b0e4ce0d87

tdf#164969 tdf#165297 Disable theming by default
    commit 924c7de80afa47a93705e5d073c35f2d81f4ed5a
    Date:   Wed Dec 25 23:13:47 2024 +0530

        tdf#164393 [API CHANGE] Make the "Automatic" theme Customizable

had - among others - enabled theming by default, which
results in incorrect colors being used with at least
GTK and Qt based VCL plugins on Linux in the default
configuration, i.e. without any custom color having
been set anywhere.

As discussed in [1], disable theming again by default, by
setting the default for
`officecfg::Office::Common::Appearance::LibreOfficeTheme`
to 0 again.

This implies that custom colors for widgets cannot be
set in "Tools" -> "Options" -> "Appearance" by default
anymore.
In order to set custom colors for those, the above-mentioned
setting can still be set to 1 in the expert settings
(in which case colors can be set for the "Automatic"
theme also, which was implemented in the above-mentioned
commit).

A larger rework of the theming code is in progress,
see Sahil's WIP Gerrit change at [2].

[1] https://gerrit.libreoffice.org/c/core/+/183490/comments/efc32644_52e556d5
[2] https://gerrit.libreoffice.org/c/core/+/183574

(In reply to Saburo from comment #2):

That commit disables theming by default for now, because the current state of theming breaks the default appearance at least for GTK and Qt based UIs. To enable it again, you can follow the steps described in the commit message:

> As discussed in [1], disable theming again by default, by
> setting the default for
> `officecfg::Office::Common::Appearance::LibreOfficeTheme`
> to 0 again.
> 
> This implies that custom colors for widgets cannot be
> set in "Tools" -> "Options" -> "Appearance" by default
> anymore.
> In order to set custom colors for those, the above-mentioned
> setting can still be set to 1 in the expert settings
> (in which case colors can be set for the "Automatic"
> theme also, which was implemented in the above-mentioned
> commit).

Enabling it by default again (or finding a different solution) depends on Sahil's current ongoing work.

Seems, to get it to work, these two options must be changed in the advanced settings for now:
org.openoffice.Office.Common 
Appearance        LibreOfficeTheme           short      1 
Appearance        ApplicationAppearance      short      1

As LibreOffice 25.8 alpha 1 has been released, a mention of this in the release notes, I think, would be nice.
https://qa.blog.documentfoundation.org/2025/05/20/libreoffice-25-8-alpha1-is-available-for-testing/

https://cgit.freedesktop.org/libreoffice/core/commit/?id=22a8a7583c5e906a7a5ecac97b34e2beca506389
fix the issue.