I think there should be 2 discussions,one about Illyrian language- Albanian language continuity and another one about Illyrian genetics-Albanian genetics continuity.
There is no connection between Albanian and Illyrian. It was mistake Albanian scientists in time of Enver Hoxha. Albanian authorities from that time loved this hypothesis.
(Albanian scientists in time of Enver Hoxha were mistaken, trying to prove unprovable.)
But science has long refuted this hypothesis.
For example you can read in The prehistory of the Balkans, edited by John Boardman, Cambridge University Press:
Page 848
"...Illyrian and Phyrgian should be classed as Centum languages".
"On the one hand Thracian, and Dacian have one of the main Satem characteristics..."
...
And we know that
Albanian is Satem.
Science says that
Illyrian and Albanian belong two different branch of IE language making them mutually exclusive of one another.
Reputable Albanian linguists Bariqi, Çabej etc. write it in scientific papers.
Illyirian and Albanian languages have no connection, two different IE branches, and Illyrians and Albanians have no connection.
It is the end.