If I have Captain Farron and a recruit token in base, does the recruit lose assault as it moves from base to a battlefield alone?

Yes, the Recruit token loses the [Assault] keyword as soon as it moves from your base to a battlefield.

1. The Source of the Ability

Captain Farron has a passive ability: "Other friendly units here have [Assault]."

• "Here" refers to the location where Captain Farron is currently present (Rule 053.3).
• Because this is a passive ability, it is a continuous effect that only applies to units that are at the same location as Captain Farron.

2. The Movement

When the Recruit token moves from your base to a battlefield:

• The Recruit token is no longer at the same location as Captain Farron.
• As soon as the Recruit token leaves the base, it is no longer "here" relative to Captain Farron.
• The passive ability granted by Captain Farron immediately ceases to apply to the Recruit token.

3. Clarification on [Assault]

• The Recruit token had the [Assault] keyword while it was at the base with Captain Farron.
• The moment it moves to a different location, it loses that keyword because the condition for the passive ability ("here") is no longer met.
• It does not matter if the Recruit token moves alone or with other units; the determining factor is whether it is at the same location as Captain Farron.

Summary

According to Rule 361 (Passive Abilities), these abilities are statements of fact that affect the game state. Since Captain Farron's ability is conditional on the unit being "here," the moment the Recruit token moves to a battlefield, it is no longer "here," and the [Assault] keyword is removed from the Recruit token's characteristics.

Note: I could not fully verify this ruling against the retrieved rules.