Horizontal diffusion coefficients

I use NEMO 4.x with the options
ln_traldf_blp = .true. ! bilaplacian operator
ln_dynldf_blp = .true. ! bilaplacian operator
In my case eddy coefficients of viscosity and diffusivity are
ahm = 1/12 UvLv^3
aht = 1/12 Ud
Ld^3.
As far as I understand, the model needs only ahm, aht values, U and L values are not used.
E.g. NEMO with Uv = 0.001, Lv = 1e+3 gives the same results as NEMO with Uv = 1, Lv = 1e+2.
Am I correct ?

Also, which values of ahm, aht should be used with 1-km resolution ?

In NEMO 3.6, one would set ahm and aht in the namelist_cfg. However, in NEMO 4.x we instead set Ud and Ld. You are correct that, in your case, U=0.001, L=1e3 gives the same aht as U=1, L=1e2.
Myself, I usually set Ld and Lv to the grid size, and then modify Ud, Uv to get the aht, ahm that I want.

It’s hard to say what are appropriate ahm and aht for a 1-km resolution since there’s a lot of tuning that goes into these parameters. I used -1.25e11 for ORCA12. You could aim for a viscosity (ahm) that is around -2.5e8 i.e. 1/8³ of the ORCA12 number. For aht, you could consider 0 at first and then see if any diffusion is needed.