> It more has to do with how many crop tiles you are allowed to place into occupied fields
per planting action.
(emphasis mine)
Here's how I read that, as an example;
Turn 1: Assume all fields are empty. Player A (who has the regular hoe) pays 4 gold and plants 4 crops: parsnip (slot 2), potato (3), strawberry (4), and cauliflower (5). The player then waters the crops (shifting everything down one but not collecting anything) and returns home to upgrade to a Copper Hoe (stack 1 crop).
Field state:
Slot 5 | Slot 4 | Slot 3 | Slot 2 | Slot 1 |
Empty | Cauliflower | Strawberry | Potato | Parsnip |
Turn 2: Player A pays 2 gold to plant 2 crops: cauliflower (5), and a parsnip (on slot 2, even though there is a potato there) using the Copper hoe. Player A then does something else and returns home, not upgrading the hoe.
Field state:
Slot 5 | Slot 4 | Slot 3 | Slot 2 | Slot 1 |
Cauliflower | Cauliflower | Strawberry | Parsnip
Potato | Parsnip |
Turn 3: Player A pays 1 gold to plant 1 crop, electing to place another Parsnip in slot 2. The player then waters the crops (collecting the single parsnip and shifting everything down one). Upon returning home, the player upgrades their tool to an Iron Hoe.
Field state:
Slot 5 | Slot 4 | Slot 3 | Slot 2 | Slot 1 |
Empty | Cauliflower | Cauliflower | Strawberry | Parsnip
Parsnip
Potato |
Turn 4: Player A pays 3 gold to plant 3 crops, electing to place two cauliflower in slot 5 - the first because it's empty, the other one thanks to the upgraded hoe. The player would like to be able to place a 3rd cauliflower into slot 5
as the hoe allows them to do, but all four cauliflower tiles are already in play. The player places a strawberry (4) instead.
Field state:
Slot 5 | Slot 4 | Slot 3 | Slot 2 | Slot 1 |
Cauliflower
Cauliflower | Strawberry
Cauliflower | Cauliflower | Strawberry | Parsnip
Parsnip
Potato |
And so on. With the current field state, only the player with the upgraded hoe could plant anything at all. With the Iron Hoe, that means that Player A would be able (if no watering is done) to plant 2 fields each planting action. They would be able to do this until each crop reached the 4 tile limit.
The hoe upgrade is more about the efficiency of the planting action (making the most of a single action) than it is about field capacity (limiting available resources). This is true of all the other tools as well - the watering can allows more efficient watering, the fishing rod allows more success at (e.g.; efficient) fishing, and the pickaxe allows more success at mining.