Every scope, digital and analog, will have retrigger time. Digital scopes will have slower retrigger time because they have to process captured data before proceeding with new capture.
What you're trying to do won't work well on pretty much any digital scope. It might work better on some (Keysight Megazoom based scopes that claim high wfm/s numbers like 3000/4000/6000 series) but even that only on lowish frequencies.
Also, that trig out frequency might not be very stable (it will have jitter) because in most digital scopes nowadays trigger is not analog comparator connected to sweep circuit, but a digital pattern engine working off a digitized data from A/D converter (hence digital trigger). So not only that it will be quantized to sampling clock of the scope, but it will have some delay to output and that one might not even be constant, depending of what is scope doing or what trigger you are using, so it will vary and you end up with jitter on trigger out.
What you are trying to measure with digital scope and counter is not a proper way to measure frequency .
Some analog scopes had outputs from their vertical amps so you could connect other equipment (like counter in your case) using scope as a sort of preamp (that was cool, I miss that). Also, their trigger circuit was analog comparator connected to sweep circuit, and by virtue of that completely synchronous to input signal. So you could measure frequency by measuring trig out, but even then you could do that for maybe 100s of Khz(depending on scope). It would work for your specific case, but not good universal practice even then.
Today's digital scopes have none of that.
That is a crux of many discussions here about scopes. New digital scopes are not only digital. They are different and should be used differently that analog scopes.
This is one example of what digital scopes cannot do. On the other hand , my Keysight scope has same order of magnitude stability of TCXO compared to my TF930 counter so most of the time I just use counter built in to the scope to measure frequencies. More than enough for most of the work because it is better than any normal crystal oscillators (that are order of 10s of ppm) and anything that isn't high end TCXO, OCXO, rubidium, cesium or GPSDO frequency source.
If I need more precision that 8 digits, (or like you trying to check and/or calibrate watch crystals and need reciprocal counting for that), then I connect counter directly and pay more attention...
On clock chips, and Atmel AVR processors I enable clock out and measure that. It gives nice buffered strong signal that is easy to measure directly with counter.