MSSQL recursive query to find furthest parent - sql-server

Question

We have a db structure where each company has a parent company defined. What we want to do is walk up the structure from a given start point until the next 'most-parent' company is found and pull what that users assignment is to that 'most-parent' company. Below is a mock example.
+===================+ +=======+ +=============+
| Company | | User | | UserAccess |
+===================+ +=======+ +=============+
| id | | id | | id |
| Name | | Name | | fkUserId |
| fkParentCompanyId | +=======+ | fkCompanyId |
+===================+ | AccessLevel |
+=============+
+=======+
|Company|
+=============================================+
| id | Name | fkParentCompanyId |
+=============================================+
| 1 | ABC Corp | 1 |
| 2 | Outside Company | 1 |
| 3 | Inside Company | 1 |
| 4 | My Company | 3 |
| 5 | Other LLC | 4 |
| 6 | Yet Another Comp | 5 |
+=============================================+
+====+
|User|
+======================+
| id | Name |
+======================+
| 1 | Mike |
| 2 | Jackie |
| 3 | Sam |
+======================+
+==========+
|UserAccess|
+=================================================+
| id | fkUserId | fkCompanyId | AccessLevel |
+=================================================+
| 1 | 1 | 1 | Administrator |
| 2 | 2 | 1 | User |
| 3 | 3 | 1 | Administrator |
| 4 | 3 | 3 | Parent |
| 5 | 3 | 4 | Parent |
| 6 | 3 | 5 | Parent |
| 7 | 3 | 6 | Parent |
+=================================================+
So take 'Same', user.id == 3. I want to do a query that finds the nearest "not-Parent" relationship when given a starting Company.id along with Sam's User.id. Next is what I'm looking to get from the given inputs.
Inputs: User.id = 3, Company.id = 6
Output: Administrator
Inputs: User.id = 3, Company.id = 5
Output: Administrator
Inputs: User.id = 3, Company.id = 4
Output: Administrator
Inputs: User.id = 2, Company.id = 1
Output: User
I've been looking at recursive queries using the CTE model, having some difficulty understanding what's it's really doing and thus not yet able to translate that model into something that would work for the above example.
Any guidance would be greatly appreciated.
Update
Been working on CTE in SSMS and feel like I'm getting close... Here is an example query that I'm trying, but not getting the result I expect...
Here I'm trying to do a recursive CTE on Sam # "Yet Another Comp". What I want is a list of Sams access up the chain.
with cte(UserId, CompanyId, UserAccess, ParentCompanyId)
as
(
select
[UserId],
[CompanyId],
[UserAccess],
[ParentCompanyId]
from [UserAccess]
where [UserId] = 3 and [CompanyId] = 6
union all
select
[UserAccess].[UserId],
[UserAccess].[CompanyId],
[UserAccess].[AccessLevel],
[cte].[ParentCompanyId]
from [UserAccess]
join [cte] on [UserAccess].[ParentCompanyId] = [cte].[CompanyId]
where [UserAccess].[UserId] = 3 [UserAccess].[CompanyId] != 6
)
select * from cte
I'm expecting this:
+===+
|cte|
+==========================================================+
| UserId | CompanyId | UserAccess | ParentCompanyId |
+==========================================================+
| 3 | 6 | Parent | 5 |
| 3 | 5 | Parent | 4 |
| 3 | 4 | Parent | 3 |
| 3 | 3 | Parent | 1 |
| 3 | 1 | Administrator | 1 |
+==========================================================+
But what I'm actually getting is this:
+===+
|cte|
+==========================================================+
| UserId | CompanyId | UserAccess | ParentCompanyId |
+==========================================================+
| 3 | 6 | Parent | 5 |
+==========================================================+
The recursive query isn't pulling additional rows into the table. So I commented out the where statement on the recursive query, expecting to get a max recursion error and see a blip of all of the results. But no, still just get the single row back.