P: Ability to sync Lightroom Classic keywords with the Lightroom Ecosystem

... so we’ll see a good LR update in October, I guess

I totally agree.  I can appreciate the artificial inteiligence and the assigning objects that Lightroom recognizes, but this is not perfect by any means.  I thought one of the objectives of Lightroom is to give the user control over their catalog and have the flexibility needed for their system, not impose Adobe's thinking.  Given Lightrooms intentional limitation, i will just have to work around that, though i don't like it, simply use the mobile cc version for just showing friends and family, not for working, because despite what they say, without keywords, it's useless to use mobile for working on assets.

I'm using iCloud, 2TB I can use the way I want for 10€/Mo.
It works. 
With C1 I can grab a session on my second computer.

About cloud, have a read here : https://www.on1.com/products/2020-preview/

Sync services arrive at the competitor. No closed cloud. No monthly fee (at least for the software), I don't know for the service sync

Just storing your files in Dropbox-like folders (which C1, LR or any other app can do) and adopting a Bridge-style folder-based workflow isn't remotely the same as having a cloud-based mobile toolset like Lightroom iOS/Android/Web which lets you make adjustments and add (some) metadata.

The cloud -despite its bug and limitations- is literally the only thing keeping me with LR. How do you work with cloud?

 I've switch to C1. Not perfect but the way the session works, the fact I can use it for as long I want, the way I can use my own cloud fit perfectly my needs.

Exactly

Once again, you’ve proved it’s not a technical issue but a marketing decision.

It is really easy to understand.
Adobe does not want you to manage your keyword. As far your use Classic, you are in control. As far you use mobile, you lose control on your asset. Everything is done you can't use Classic and mobile in conjunction to make your asset virtually "captive". 
So Adobe will not make it. You have the choice of using the old and slow Classic or the new and fast but weak mobile.
Pay may friend, pay.

Even keeping the constraint that LR Classic uses hierarchical KW's and LR Cloud uses a linear (flat) KW structure, this problem can be solved.  There are, of course, some technical aspects but the main rationale I've heard so far for not doing this is the logical problem of how to map a hierarchical structure to a linear structure.  One solution is to convert LR Cloud to a hierarchical structure but putting that aside, here is one possible solution to that problem:

1)  In LR Classic, Adobe can add check boxes in the create/edit keyword dialog for

• "Sync this KW with LR Cloud"
• "Sync Containing KW's with LR Cloud"
• "Sync Synonyms with LR Cloud (would become regular KW's in LR Cloud)

2)  When a user ticks any of these boxes, LR Classic would check to assure that it is not redundant.  For example.  If you already ticked KW "Red" under "Flowers", and now you are trying to tick keyword "Red" under "Cars": it would reject the request as a duplicate.  By doing this, it will enforce a one to one correspondence between ticked KW's in LR Classic and KW's in LR Cloud - thus allowing two way sync

3)  If an image in LR Classic gets or loses a keyword with one or more of these ticked boxes, or the tick's get changed, that change can be placed in the Smart Preview (or XMP data) and can sync to LR Cloud.  This may include adding the KW to LR Cloud, adding an LR Cloud KW to the image or removing a KW from the image in LR Cloud

4)  If a user defined KW is added to an image in LR Cloud it could map to either no KW's in LR Classic or at the most to one "ticked" KW in LR Classic.  In the former case, LR Classic would create the new KW at the root level of the Hierarchy with "Sync this KW with LR Cloud" ticked.  In the later case there would be only 1 ticked LR Classic Keyword with that name that would be affected.

THIS CAN BE DONE if there is a will to do so at Adobe and the more people who "vote" for having KW's sync between the ecosystems, the more it will push Adobe to re-consider this.