Correct syntax for random coefficient in Cox with time-varying predictors using R coxme

thanks for helping!

I am testing a repeated measures dataset (multiple rows per participant) in a multilevel Cox regression with time-varying predictors. I'm trying to see if effects vary by assessor. My variables are:

• ID: participant ID (time independent)
• dynamic: repeated measure test score (time dependent)
• assessor: person doing assessment, nesting variable (time independent)
• intervention : binary, whether or not dynamic was followed by intervention (time dependent)
• entry: beginning of prediction interval (time dependent)
• exit: end of prediction interval (time dependent)
• flag: if survival event occurred during interval (time dependent)

I want to eventually test if interactions between dynamic and intervention vary by assessor, but starting with univariate tests, I have two questions.

First: I keep seeing two separate ways of specifying that I want the slope (of "dynamic")to vary by assessor. What is the difference between

model<-coxme(Surv(entry,exit,flag)~dynamic+(1+dynamic|assessor),data=data)

and

model<-coxme(Surv(entry,exit,flag)~dynamic+(1|assessor/dynamic),data=data)?

Second: Does it make sense to test a random coefficient for a binary variable? Would that use different syntax? Would random effects be interpretable or would I go by chi-square of the models?