Simply put, it's because RRDv5 deals only in matching the path, not any part of the query search string.
For route path matching, only the "/support_main/notice" is considered. To make this a bit more clear, here is a more conventional way to link to "/support_main/notice" and pass a search string. Here the path and search string are split up and explicitly passed.
<Link
to={{
pathname: "/support_main/notice",
search: "?page=1"
}}
>
To notice
</Link>
When you link to "/support_main/notice?page=1" the search isn't part of the path matching.
Link to-object
to: object
An object that can have any of the following properties:
pathname: A string representing the path to link to.
search: A string representation of query parameters.
hash: A hash to put in the URL, e.g. #a-hash.
state: State to persist to the location.
<Link
to={{
pathname: "/courses",
search: "?sort=name",
hash: "#the-hash",
state: { fromDashboard: true }
}}
/>
Consider the following code:
const Page1MatchPath = () => <h1>Page 1 matched by path</h1>;
const Page1MatchPathAndQuery = () => <h1>Page 1 matched by path and query</h1>;
export default function App() {
return (
<Router>
<div className="App">
<h1>Hello CodeSandbox</h1>
<h2>Start editing to see some magic happen!</h2>
<ul>
<li>
<Link to="/support_main/notice?page=1">To notice (string)</Link>
</li>
<li>
<Link
to={{
pathname: "/support_main/notice",
search: "?page=1"
}}
>
To notice (object)
</Link>
</li>
</ul>
<Switch>
<Route
path={"/support_main/notice?page=1"}
component={Page1MatchPathAndQuery}
/>
<Route path={"/support_main/notice"} component={Page1MatchPath} />
</Switch>
</div>
</Router>
);
}

Note that even though the full path and query string is listed first in the Switch that is doesn't match, and is skipped over and matched by path alone. In other words, it's too specific to match "/support_main/notice", and yet doesn't take the query string into consideration for matching.
But why don't query strings work in path prop?
This is very likely due to the way path matching is handled. Under-the-hood RRDv5 path props are strings that path-to-regex@^1.7.0 understands. In this specific case the "?" character is interpreted as an optional parameter.
Optional
Parameters can be suffixed with a question mark (?) to make the
parameter optional. This will also make the prefix optional.
var re = pathToRegexp('/:foo/:bar?', keys)
// keys = [{ name: 'foo', ... }, { name: 'bar', delimiter: '/', optional: true, repeat: false }]
re.exec('/test')
//=> ['/test', 'test', undefined]
re.exec('/test/route')
//=> ['/test', 'test', 'route']
To also more firmly put it, the Usage outright also states in a note:
Please note: The RegExp returned by path-to-regexp is intended for use with pathnames or hostnames. It can not handle the query
strings or fragments of a URL.