Longitudinal Mulitlevel Model and Complex Survey Design in R Studio

I'm using multiple waves of the United Kingdom Household Longitudinal Survey (also known as "Understanding Society Survey") and want to use mulilevel models to explore change in health within individuals and between individuals. As far as I understand using a simple two-level model would mean that:

Level 1 is time/wave
Level 2 are individuals

But considering currently there is no way to account for the complex survey design for multilevel modelling on R as far as I know (happy to be told that I am wrong) I am now wondering if I just ignore the survey design or how else I can account for it?

The sampling strategy for the UKHLS is a very complex multi-stage sampling strategy and entails stratification and clustering to find addresses from which all people in the household are then chosen. Strata and PSU variables exist so I could theoretically use them but I'm not sure if I should?

Should I just add them as other levels in the model and would household then also need to be added as a level?

Like this for example:

Level 1 = time/wave
Level 2 = individuals
Level 3 = Household/ PSU
Level 4 = Strata
I am not actually interested in changes in health between housholds, or regions of the country but simply don't want to ignore the survey design unless that's fine for interpretation.

Another question I have is regarding weights and how to include them. According to the User guide UKHLS data is meant to be used with weights and the data sets provide weights that are described like this in the User guide:

Weights are constructed by combining (i) design weights which adjust for unequal selection or sampling fraction and(ii)non-response weights which adjust for differential non-response and attrition at various stages (household level, within household at individual level, whether adult respondent completed self-completion questionnaire or not).

As far as I know in multilevel modelling if one wants to account for weights one needs weights for each level but while there is a weights for individuals there is none for time as far as I know. So do I just weight it using the one weight and if so how or what do I do?

Thank you!