How to interpret a variable

I'm not familiar with the format '${state.Objektiv}' - that is not how variables are used in MSSQL. See Variables (Transact-SQL) | Microsoft Docs[^].
The $ symbol isn't listed as a Symbol that would be used in MSSQL - SQL Symbol Cheat Sheet[^]

Does this example help you -

declare @tblFoto table (Bildnr int) -- You won't need this bit if you already have your table
declare @state_Objektiv varchar(255) = 'Fahrzeugdatenträger'
declare @Bildnummer int

set  @Bildnummer = (SELECT 
CASE @state_Objektiv
    WHEN 'vorne rechts' THEN 2

    WHEN 'vorne links' THEN 3

    WHEN 'hinten rechts' THEN 4

    WHEN 'hinten links' THEN 5

    WHEN 'Innenraum' THEN 6

    WHEN 'Navigationsgerät' THEN 7

    WHEN 'Kombiinstrument' THEN 8
    
    WHEN 'Fahrzeugdatenträger' THEN 9
    
    WHEN 'Servicenachweis' THEN 10
    
    ELSE 11
END)

insert into @tblFoto (Bildnr) values (@Bildnummer)
select * from @tblFoto

EDIT - @Naga-Sindhura has pointed out that that is a long list of conditions that are probably better handled using a table variable. e.g.

declare  @references table (Beschreib nvarchar(255), bildnr int)
insert into @references (Beschreib, bildnr) values
('vorne rechts',  2),
('vorne links',  3),
('hinten rechts',  4),
('hinten links',  5),
('Innenraum',  6),
('Navigationsgerät',  7),
('Kombiinstrument',  8),
('Fahrzeugdatenträger',  9),
('Servicenachweis',  10)

Note I have not added an entry for the ELSE condition (11).
Then you can do something like

declare @tblFoto table (Bildnr int)
declare @state_Objektiv varchar(255) = 'FahrzeugdatenträgerXXX'
declare @Bildnummer int = (SELECT bildnr from @references WHERE Beschreib = @state_Objektiv)
insert into @tblFoto (Bildnr) values (ISNULL(@Bildnummer,11))
select * from @tblFoto

Notice the use of ISNULL to handle what was the ELSE condition