which Model to apply on panel data where unique id has 6-8 records and total records are 2,000,000?
Your data is a good candidate for a mixed effect model.
You have two potential random effects that look to be crossed: I see ID as one and state as another, as it seems that any ID can belong to any state.
Essentially, you can leverage the fact that some states and some IDs will have less data than others (and in general, some states and IDs will vary more than others). States and IDs who exhibit such characteristics will have their predictions bolstered by other states and IDs (called partial pooling). You also need to use time as a variable (perhaps convert quarter to 2019.25, 2019.5, etc. or use two time variables year, quarter) because you wish to predict the next period.
I think generalized linear mixed effect models can scale to 2 million observations. There are also machine learning methods that allow for mixed effects: mixed effect random forests (MixRF), mixed effect gradient boosting (GPBoost/mboost), and of course you can go full Bayesian as well (though you will likely need to use an approximation method since your data is large). The ML models may scale better.