Windows can store some properties for apps when you restart them. Like the size and position. My guess is, that somehow that was screwed up for the download window. According to your screenshot it is not a tab. It is a separate window, or it would not have a separate icon in the task bar.
Did you try moving your mouse to the lower right corner of the download window? Does the cursor change to indicate resize option? Can you resize the window? If not, activate the download window and press the windows-key and the up-arrow-key together.
I disable scroll bars in browsers with a custom style. This has nothing to do with your problem. I just commented how ugly they look to me. Especially with a dark theme. The itch browser is chromium, but unless they allow extensions, I think that could not easily be done there. In a regular browser I would edit the custom css file, or just use one of the simple user style extensions and put this as a global style
element::-webkit-scrollbar {
display: none;
}
::-webkit-scrollbar {
display: none;
}