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Fungi growing around your Lavender can indicate your plant is not receiving enough sunlight and with both root rot and the fungi, I would say you are over watering or your soil is poorly draining.
Make sure you are not overwatering your plants.
You may need to transplant your Lavender to a location that is better suited.

Here are some links to refresh you on the care requirements.

https://www.gardeningknowhow.com/edible/herbs/lavender/lavender-in-the-garden-information-and-growing-lavender-tips.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/what-is-well-drained-garden-soil.htm

Here is a link with care information.

https://www.gardeningknowhow.com/edible/herbs/lavender/growing-lavender-in-pots.htm

This article will help you.

https://www.gardeningknowhow.com/ornamental/fungus-lichen/what-is-slime-mold-slime.htm

The leaves look fine, it is just the blooms turning brown because they are done. Remove the spent blooms/spikes and the plant will reward you with more blooms later. As you know clay is not good for lavender but yours looks healthy now. I would do hard pruning in the winter, before the plant breaks dormancy. You can trim it anytime.

Lavender is a woody plant and needs to be pruned annually or the woody stems get thicker and less productive. Plus the plant looks sloppy/floppy. I have selectively removed overgrown stems to open up the plant and let more sunshine in. Hard pruning is typically done when the plant is dormant in winter. My sister cut them to the ground, not knowing what else to do and the plant came roaring back the next spring. Did you trim off the spent blooms? There may be growth underneath that you can't see. Lavender doesn't like a lot of water so that is not a solution. I confess to starting from seed again when I was an inexperienced gardener. It is easy to grow from seed, in my opinion. It doesn't germinate rapidly so patience is key.

During the heat of summer is the most stressful time to move plants, from the plants point of view. If any of your plants is now in a pot, transplanting is simpler and OK. Water when the soil is dry, mulch and provide shade for several days as the roots develop in their new home. If you are digging plants from the ground, you will inevitably cut some of the feeder roots. To compensate, cut the topgrowth by at least a third, more if the plant wilts badly. Unless the bloom is over, I would not transplant the bulbs. Even so, you risk losing vigor since the bulb will not be able to renew itself as well if transplanted now. Remember that lavender likes sun but looser soil and not as much water as the others you mention. All except astilbe like full sun, 6+ hrs of direct sunlight daily. Astilbe likes protection from afternoon sun and will often develop brown edges, if not go dormant, in hot, full sun.