Pesach has Yom ha’Atzmaut, as both entail a new founding & Liberation.
No, you are reading the A”t Ba”sh wrong. He notes that the first day of Pesach’s At Bash is Tisha B’av. The corresponding holiday should be the one that corresponds with the first day of pesach.
And the connection is that they are both about reshaim taking over eretz yisroel.