No. Adobe's technical requirements for InDesign list 64-bit Windows 10 and Windows 11 and recent macOS only. There is no Linux version and no browser version of InDesign.
Adobe InDesign by Adobe · Design, CAD & 3D · No way to run it
Adobe's own requirements page for InDesign lists Windows 10 and Windows 11, both 64-bit, alongside
macOS. Linux is absent, as it is for every Creative Cloud program. Adobe has put some of its other
products in the browser, but page layout is not one of them, so there is no web version to fall
back on the way there is with Acrobat.
If you produce documents for a living, this is one of the harder losses in the whole switch. The
free layout programs on Linux are competent and none of them matches InDesign for typography,
long-document handling and, most of all, for working with printers and other designers who expect
InDesign files.
Your .indd files do not travel. No Linux program opens one, and there is no reliable converter.
Before you leave Windows, open every document you might need again and export two things: a
print-ready PDF, which preserves exactly how the page looks, and an IDML file, which is InDesign's
exchange format and is the only version another layout program has a chance of reading. Even then
expect fonts, styles and image links to need repair.
For simple layout work on Linux, LibreOffice Writer handles newsletters, reports and manuals
reasonably. Inkscape is better for single pages such as posters and flyers, where typography and
precise placement matter more than flowing text across pages. Neither is InDesign, and if
commercial print work is your trade you should plan to keep a Windows or Mac machine.
Better for single-page pieces such as posters, flyers and covers, with precise control over type and placement. No flowing text across pages.
Your files: Cannot open .indd. Can open PDF exports, which gives you editable shapes and text but a broken version of the original layout.
This doesn't have to stop you
One stubborn program doesn't have to decide the whole question. You can keep Windows on the same PC and restart into it only when you need Adobe InDesign. Everything else you do can move.