Does the 'making spells cheaper' effect from Eager Apprentice at a battlefield offset the increase in energy cost (not power) caused by Vex's effect? Even if the spell was 1 energy base. My impression is that it's not a trigger effect so it doesn't 'snapshot' like buffs/debuffs do and only checks for if the minimum value of 1 is reached.

To address your question regarding the interaction between Eager Apprentice and Vex, Cheerless, we must look at how cost modifications are applied in Riftbound.

The Ruling

Yes, the cost reduction from Eager Apprentice can offset the Energy cost increase from Vex, Cheerless. However, because Vex's effect also increases the Power cost, the final cost of your spell will be affected by both.

According to Rule 353, cost modifications are applied in a specific sequence: increases (Rule 353.3) are applied before discounts (Rule 353.4). Because Eager Apprentice's discount has a "minimum of 1 Energy" restriction, the order of operations ensures the final cost is calculated based on the total modified value.

Example: Playing a 1-Energy Base Cost Spell

If you play a spell with a base cost of 1 Energy + 0 Power while you control an Eager Apprentice and your opponent controls a Vex, Cheerless:

1. Start: Base cost is 1 Energy + 0 Power.
2. Apply Vex (Increase): The spell's cost increases by 1 Energy + 1 Power. The new cost is 2 Energy + 1 Power.
3. Apply Eager Apprentice (Discount): You reduce the Energy cost by 1.
   • Note: Eager Apprentice's discount has a "minimum of 1 Energy" restriction.
   • Applying the discount to the 2 Energy cost results in 1 Energy + 1 Power.

Final Cost: 1 Energy + 1 Power.

Key Mechanics

• No Snapshotting: These are continuous effects that apply during the Determine Total Cost step (Rule 353).
• Minimum Restrictions: As clarified in Rule 353.4.c and FAQ 8597, the "minimum of 1" restriction applies to the specific discount providing it. You cannot reduce the Energy cost below 1 if a "minimum of 1" restriction is active on that specific discount.
• Power Costs: Vex, Cheerless specifically increases both Energy and Power costs for enemy spells. Eager Apprentice only reduces the Energy cost. Therefore, even if you reduce the Energy cost to its minimum, the Power cost increase from Vex remains.

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