How to hide custom picker field and display a textbox for creating new record when there is no matching data in selection

One note to add here is that how I sometimes implement this is by appending the search itself to the custom picker datasubset, so that if it is not present, it can still be selected within the same picker.  Downstream logic can identify if this entry is new or not.

This snippet is from a Meeting Minutes app I have where meetings are linked by topic, if a new topic is being added it can be done via the same custom picker even if no related meetings are present:

/* local!data from a!queryEntity().data */

  local!topics: append(property(local!data,"topic",null),ri!search),
  
  local!distinctTopics: reject(fn!isnull,rule!APN_distinct(local!topics)),
  local!top10: index(local!distinctTopics,enumerate(min(10,length(local!distinctTopics)))+1,null),
  a!dataSubset(
    startIndex: 1,
    batchSize: 10,
    totalCount: length(local!distinctTopics),
    data: local!top10,
    identifiers: local!top10
  )

By that same logic I suppose you could hard-code a selection along the lines of "<New Entry>" to always appear along with search options, and if that one is selected, trigger additonal on-form logic to type in text/etc (allowing for additional instructions and/or validations perhaps).  Honestly I haven't messed with this very much, other than a reusable component I made a long time ago to replace a people picker box with a people-from-DB-table picker (allowing even deactivated usernames to be chosen).

By that same logic I suppose you could hard-code a selection along the lines of "<New Entry>" to always appear along with search options, and if that one is selected, trigger additonal on-form logic to type in text/etc (allowing for additional instructions and/or validations perhaps).  Honestly I haven't messed with this very much, other than a reusable component I made a long time ago to replace a people picker box with a people-from-DB-table picker (allowing even deactivated usernames to be chosen).