Just my opinion, but I'd be looking to incorporate plenty of bulky organic matter, manure, pelleted chicken poo, which will improve the clay soil as well as feeding your plants, rather than using inorganic fertilisers which do nothing for the soil.

For your clayey soil, I would add sand as well as organic matrerial. I store my cannas in a bucket of sand I get at the local lake & add this to my planting area every year - they have been growing amazingly for five years now

I've been adding sand and compost to our clayish soil. Canns love wet feet but also need to drain a bit. After they die back I dig them up, divide them and add more soil so every year the beds get a bit higher. Sand can also help keep snails away from cannas.

I thought sand added to clay soil turned it into a harder substance reminiscent of cement? I would add organic materials such as a good bag of soil amendment, steer manure, garden soil, coffee grounds, etc. Here in AZ putting sand anywhere near our clay soil is like putting cement shoes on someone, a baggie over their body, and then watering. No water even gets to the roots, and the plants die.

You can use fish & seaweed emulsion as a fertilizer, too, & even spritz it on the leaves.

The best things I've found to loosen my asphalt-like alkaline clay are organic material & roots:
plant lots of plants!

I live in AZ, and yes sand added to clay does make the clay more like cement when it dries, BUT if you add enough, it'll improve the drainage. Make sure you add a lot and also it should be coarse sand, not the finer grain sand that compacts easily. Along with it add compost/manure/mulch. This is what I do to all of my garden beds, and it makes them so much better. Then I dump old leaves/cuttings over the beds each fall/winter.