No. Notepad is part of Windows and does not exist on Linux, but every Linux desktop comes with its own plain text editor that does the same job and opens your .txt files straight away.
Notepad by Microsoft · Utilities · No way to run it
Notepad has been bundled with Windows since the 1980s and Microsoft has never shipped it separately, let alone
for Linux. There is nothing to install and nothing to buy.
The replacement is already sitting on your new system. On Ubuntu and Fedora it is called Text Editor, on KDE
systems it is called KWrite, and in both cases double-clicking a .txt file opens it. They do what Notepad does,
plus a few things it took Microsoft decades to add, such as tabs and remembering unsaved work.
Your files come across untouched. A .txt file is a .txt file. The only small wrinkle is invisible: Windows
marks the end of each line differently to Linux, so a file written in old Notepad can occasionally look like
one long paragraph in an older Linux editor. Current editors handle it silently and you will not see it.
If what you actually used was Notepad++ rather than Notepad, that is a different question with a different
answer, and it has its own page.
Overkill for a shopping list, but the right choice if you were using Notepad to poke at code or config files.
Your files: Opens any plain text file and lets you choose Windows or Linux line endings.
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 Notepad. Everything else you do can move.