Try it now: Tap your hand on the desk randomly. Can you recall how many times you did it without "saying" a sequence in your head like "1, 2, 3" or "A, B, C" etc?
If yes, how far can you count? With a language it's effectively infinite. You could theoretically go up to "1 million 5 hundred 43 thousand, 2 hundred and 10" and effortlessly know what comes next.
An example of this would be when I’m lifting weights with a friend and am lost in the set/focusing on mind-muscle connection, and as a result I forget to count my reps. I am usually quite accurate when I verify with my lifting partner the number of reps done/remaining.
As OP mentioned, many people have no internal speech, otherwise known as anendophasia, yet can still do everything anyone with an internal dialogue can do.
Similarly for me, I can do “mental object rotation” tasks even though I have aphantasia.