Hi, I have called Adobe and after 3-4 hours support got nowhere. So here it goes.
If setup a custom camera profile in Lightroom Classic.(per a camera - ISO variant profile). (based on Xrite Color Checker - I get perfect color this way). I apply the profile to all imported photos via Lightroom Classic.
I then sync a collection of these photos to Lightroom CC / a lightroom collection for a client to review / or I try to edit further in Lightroom CC on my iPad.
The color profile is applied & displayed correctly on my Laptop running Lightroom Classic.
The color profile is displayed wrong (actually not applied at all) if I view online (via the Web Interface)
The color profile will not display on my iPad.
When I export the photos from Lightroom CC the color profile is wrong as well.
When I export the photos from Lightroom Classic it does apply the correct colors.
When I open the synced photo in Lightroom CC on my iPad and deselect the Custom Camera profile (say I change my EOS Camera profile to Adobe Standard, then reselect the EOS Camera profile) then the profile will display correctly and work properly.
This means the lightroom CC / lightroom web are ignoring custom profile information from Lightroom Classic. But when you apply the profile within Lightroom CC it will work correctly.
But this does prohibit sharing with other from Classic to LR CC and editing between Classic & iPad.