There's no universal way to leave the input bar always open (in the web app - technically it's always open in Teams)...
But technically an option could be to Enable NLU to switch topics (see Virtual Agent Designer user input controls (servicenow.com)) on every single (non-text) user input. It'd be very tedious going back to every topic and doing this and remembering to do it for every future topic, but it is an option.
When you enable that, it allows text input at any user input (say, a choice input) - primarily with the intent to allow users to switch topics and do small talk via NLU (i.e. if a user out of the blue types in something to trigger a new topic), though I do believe it also allows you to type the response to that input as well. i.e. it'll let you type in "yes|no" in response to a boolean input - but don't quote me on that. Personally, I would not use this setting for risk of unintended topic-switching consequences - and if I did, I'd probably prefer a universal option instead - but it is an option you have.
