Verdict: Not directly
Not directly. Adobe sells Photoshop for Windows, Mac, mobile and the web only, so nothing installs on Linux. A paid subscription does let you edit in a browser, and free installed editors cover most home jobs.
Adobe's own Photoshop page lists desktop, web and mobile versions and never mentions Linux. There is no Linux installer and Adobe has given no sign of making one. People do get older releases of Photoshop running through Wine, a tool that lets some Windows programs run on Linux, but recent subscription versions are unreliable that way and Adobe will not help you if it breaks.
Photoshop on the web is the one official route. It runs in Chrome or Firefox on Linux and needs a paid Creative Cloud subscription to open your own photos. It covers layers, masks, selections and the common retouching tools. It is slower than the installed version and the long tail of filters, plug-ins and scripting is not there.
For most people switching from Windows at home, the easier answer is a free installed editor. GIMP is the closest in scope and opens Photoshop files. Krita is better if you paint or draw. Photopea is a website that deliberately copies the Photoshop layout and opens .psd files directly, which makes it the gentlest landing spot if you only touch Photoshop occasionally.
Your .psd files are not stranded. GIMP and Photopea both open them, including layers, though very new adjustment layers and smart objects can come through flattened or slightly changed. Keep the originals rather than saving over them until you are happy with what you see.
Free and covers photo editing, layers, masks and retouching. The tools are named differently and the learning curve is real.
Your files: Opens .psd files with layers. Some adjustment layers and smart objects arrive flattened. Saves in its own .xcf format by default.
A free website laid out almost exactly like Photoshop. Nothing to install and it runs in your browser on Linux.
Your files: Opens and saves .psd files directly, with good layer support.
Free, and the better choice for drawing, painting and tablet work than for photo correction.
Your files: Opens .psd files, though complex ones lose some effects.
Small and simple, for cropping, resizing and quick touch-ups rather than serious editing.
Your files: No .psd support. Handles .jpg, .png and its own format.
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