Parks do not increase the happiness of industrial buildings.
Parks increase land value. Land value causes residential and commercial buildings to convert into wealthier versions, but only happiness will cause density upgrades. You can check happiness in the happiness data map.
To upgrade the density of the industrial building, you need to improve its happiness (aka profit) through the freight system:
First, freight must be produced. This happens when the building's needs are met and it is open. The number of workers doesn't matter as long as the building is open.
Second, freight must be delivered. Each hour, a freight truck is spawned from each industrial building (unless one is already out). The freight truck will carry freight to a building with available freight orders. The truck will exchange the freight for profit (1 for 1) and reduce the available orders in that location. The truck will then return with the profit and drop it in the building.
Buildings with freight orders include: freight warehouses, commercial buildings, many specialization buildings (such as the mine). If freight is delivered to a commercial building, it will also give a bonus to that commercial building's happiness.
Once delivered, freight decays over time and orders replenish over time.
Third: once happiness reaches the threshold, you also need sufficient room and road type to allow the density increase. Low -> Medium requires space behind the building - the building is twice as long. Medium -> High requires space (or other industrial) along the road - the building is twice as wide.
It may also be helpful to know that High density Industrial buildings will burn down without the hazmat firefighting addon.
If you're still confused, I've talked about freight and goods as related to happiness and density before.