Most - but not all - herbaceous perennials will grow up through mulch quite easily. The danger of piling mulch over the crown of the plant is that it typically is too moisture retentive, especially through winter, and create conditions that promote rotting or fungal issues. If your springs tend not to be excessively rainy, it should be fine to mulch now. Just don't pile it on too thickly.

The only other issue I'd want to consider is soil temperature. Mulch is a soil insulator so if your soil has not yet warmed up to normal seasonal growing temps, mulching now could slow that process. This can slow down the growth of those sorts of plants that prefer warm soils. I would wait until soil temperatures hit at least 50F at a depth of 4" before I'd apply mulch.

btw, your garden photos are lovely. Very nice work!

A garden bed should not be more than 4 feet in depth (if access is from at least two sides) unless you have made provision for getting in there, stepping stones at a minimum.

Whether plants grow through a mulch depends on a number of things, keep in mind that one reason for mulch is to suppress unwanted plant growth. Mulches will not just inhibit unwanted plant growth, although as some have found mulches do not do that if not properly applied. Whether the mulch applied would keep soil temperature too low would depend on how much material is put down and the density of that material. An inch or two will not have much affect on soil temperature or on suppressing that unwanted plant growth while the 4 inches needed would adversely affect both.

kimmq is kimmsr