Okay then, there is something odd going on. You *should* have level 2 spell slots.
I respecced a hireling to check this out. Level 4 EK does gain a spell slot at level 4, which implies that it is ESL 2 at that level. However, when I start as lvl 2 paladin then lvl 4 EK does not add an ESL, and 2 paly 4 EK remains ESL 2.
The problem isn't that they don't have 5 lvl 1 spell slots (that isn't how casters levels progress) the problem is that they don't have 4 lvl 1 and 2 lvl 2, which is what they should get at ESL 3.
I suspect that something goofy is happening with the rounding of the levels. In BG3 paladin levels are supposed to round up for ESL. It looks like EK levels do too. Maybe when they are combined the rounding is bugged?
In any case, I now believe that there is an actual problem here.
