All guilty pleas and violation of probation matters [...] must be continued until after April 13, 2020, [...]
Does this mean everything continues up to April 13th then stops or stops now and will restart April 13th?
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From Lexico continue:
2.2 US Law [with object] Postpone or adjourn (a legal proceeding)
'the case was continued without a finding until August 2'
Your sentence means:
All guilty pleas and violation of probation matters [...] must be postponed until after April 13, 2020, [...]
So, the hearings will stop until 13 April 2020, then resume (unless another emergency procedure is declared overriding this one).
Note that the US legal definition of "continue" is almost the opposite of its use in general English.
More at Wikipedia: Continuance