background blur.

As Marek says, the adjustment brush can be used to introduce blur. Selection is not as sophisticated or automated as in Photoshop, but there are some good techniques and controls in LR which can work quite well. For example: Automask especially when used with a single click of a large radius brush rather than by painting; tone or colour based Range masking.

Besides reducing sharpness and Clarity, this LR adjustment brush can apply at the same time e.g. lowered Texture / slight negative Dehaze plus saturation, tone and contrast changes that will help to pictorially enhance that differentiation of subject from background.

This assumes you are seeking a more or less simple separation of one vs the other; rather than a progressive throwing-out-of-focus. To simulate an optically shallow depth of field, Photoshop's Lens Blur can do a nice job in combination with a specially made "depth map" channel - handling the edge contours of the subject properly, in particular. Also this way slight focus differences within the subject can be included, not restricted to a background only. That takes quite a bit of artistry as well as technique, to achieve well but is IMO an enjoyable and instructive challenge to try. It's not a quick-and-dirty fix by any means though.

Lens Blur produces a quite different aesthetic look, than something that has only been blurred - in the same way that in LR, Clarity (and Texture) do something rather different, than anything achievable in the Detail panel.