sidere, sedisse...?

I’m a bit perplexed by something. In LLPSI (Cap XLIV) there is an extract from Ovid Fasti. - Libro VI.

Tullia having encouraged her husband with stirring words, Ovid tells us:

Talibus instinctus, solio privatus in alto
sederat; attonitum vulgus ad arma ruit.

Now I simply took sederat to be the pluperfect form of sedeo, sedere, sedi, sessum - ‘he had sat on the high throne’ …

Orberg tells us that it is in fact a form of the verb: sidere, sedisse.

What is this? Both L&S and Whitakkers Words give the verb (to settle down..etc..) as: sido, sidere, sidi…

How does Orberg derive a perfect infinitive for sido as sedisse …?

These forms can easily be mixed up. One has to be careful.

sĕdeō : sēdī : sessum
sīdō : sēdī : sessum*
sēdō : sēdāuī : sēdātum

But, as you noted, sīdō does also have the perfect sīdī. This is a secondary form made from the present stem. Besides, for sĕdeō we have inscriptionally even the perfect sēsī (in 3.pl.), as mentioned in the OLD.

Sēdō is factitive-causative for sĕdeō. Sīdō is reduplicated from sĕdeō with zero-grade on the stem (i.e. *si-sdō; -sd- will lengthen the preceding vowel as the s disappears).

And it goes on. For sĕdeō we have the present sedit (apparently in good manuscripts) in Venantius Fortunatus and the imperative sedito in lex tabulae Heracleensis (Iulia municipalis) from ca. 45 BCE.

*Not everyone will accept the passive perfect participle sessum for sīdō but attach all of them to sĕdeō, leaving this place blank for sīdō.

Many thanks.