Accessing Page Properties as filter for a List (List Web Part or Embed Web Part, or other)

Hello... I've unsuccessfully scoured the web for an answer to this question, so I apologize if the answer is out there and I just can't get this to work.  I have found a number of potential solutions that didn't seem to pan out, so I figured I'd start at the top and see if what I am is possible.

Some "simplified" background (capitalized and quoted words refer to Sharepoint content entities)

I have a standard set of management tools in the form of "Lists"; Action Items, Risk Management, Deliverables for example.  These "Lists" contain the data for all projects in the organization.  Each project has its own Sharepoint "Page" on the organization Sharepoint site.  Should note these are "Teams" Site/Pages.  Objective is to have a template page that can be copied when a new Project is started and limit the amount of manual configuration.

Each data "List" has a common key - Project.  In each list, the Project is a "Lookup" field that gets its value from a separate Project "List".  I didn't want to use a "Choice" field since multiple "Lists" draw from the same set of Projects and thus limiting duplicative adding of projects when a new Project starts.

What I want to do is include each "List" on a Project specific "Page" and since the lists contain data for all Projects I want to filter the list based on the Project field in the list.  If I add the "List" as a "List Web Part", the only filtering capability is "Dynamic Filtering" which connects a filter field to something selected in another library or list on the page.  With the "List Web Part" it seems the only solution is to have a "List View" preconfigured in the "List" specific for each Project and then the "View" can be selected in the "List Web Part" settings.  This solution, although it works, is not ideal since for each new program we would have to create a new "View" in each "List" for the new Project and, after copying the template "Page" edit the "View" field of every list on the page.

What I would like to do is key the filtering of the "Lists" based on the active Project "Page".  I have added a Project field to the "Page Properties" and set the field to the Project name that is in the Project list to potentially use as the filter key value in filtering the "Lists".  But I can't figure out how to make use of the "Page Property" in any of the web parts, whether trying to leverage json in some circumstances, or other potential solutions.

I have tried various things using the "List" view formatting.  The "View" filtering capability doesn't let you filter based on a "Lookup" field, but even if I did, I would still have to figure out how to reference the "Page" property that identifies the Project.

I think the closest I have come is trying to use the "</> Embed Web Part".  I can add this web part and set the website address to "https://....../Lists/AIList/AllItems.aspx?FilterField1=Project&FilterValue1=ProjectA" and it will populate the web part with the list filtered to only show the items associated with ProjectA.  But what I want is to set the FilterValue1 to the Project "Page Property".  I have seen references to page properties in various posts using @{Page.Project} (for example) or [$Page.Project] or perhaps other forms for various purposes, none of which have worked either in this "Embed Web Part" or attempts I have made in other potential solutions using json to try to control what is displayed.

Sorry for the long post, but if anyone knows a way to achieve the desired effect it would be very much appreciated.