Based on the rulebook context, specifically page 18, during the Actions Phase:

• "When it is your turn, you may take the Move and/or Trade Action as often as you want, and then you may take 1 other Action. You MUST take at least one of these. You can not skip spending an AP! Then the next player takes their turn, until everyone is out of AP."

The Trade Action (page 19) can be taken "ALWAYS," and does not end your turn. However, the rules on page 18 clarify that on your turn, you may take Move and/or Trade as often as you want, and then you may take 1 other Action. You must spend at least one AP on your turn.

If your only available AP is used to Trade for Salt, and you have no more AP left, you cannot take another action. The rule that you "MUST take at least one of these" refers to not skipping your turn without spending AP, not to being required to take a non-Trade action if you have no AP left.

Summary

• If a player’s only available AP is used to Trade for Salt, and they have no AP remaining, their turn ends after the Trade.
• The rules require you to spend at least one AP on your turn, but do not require you to take a non-Trade action if you have no AP left after Trading.

Source: page 18 (Actions Phase), page 19 (Trade Action)

Source: Core Rulebook (pp. 17, 18, 19, 20, 24)