Are there any route planning/mapping apps or websites that can show a chart of cumulative ascent?
Starting from any route-planning tool that can export GPX, you can do this on my website. It's more about the mapping and planning rides for Veloviewer Explorer, but I've added a graph showing cumulative ascent below the map that displays multiple GPXs. Multiple rides can be plotted, automatically colour coded to match the map.  Processing is handled on your own machine using javascript; nothing is uploaded to my server.  Just drag and drop the GPX onto the map.

The code is also available at GitHub under the most permissive of licenses.
Originally I took this as an interesting challenge to my spreadsheet skills.  The spreadsheet I created (xlsx, original LibreOffice ods) takes a GPX file pasted into one sheet, and displays on another sheet a graph of cumulative elevation, as well as calculating the distance at which you've done half the climbing.
It doesn't attempt to parse the XML of the GPX file; everything is done in cell formulae.  This means that each track point is assumed to look like this and to not have a timestamp (so it works for RideWithGPS and Strava routes, but not Komoot).
&lt;trkpt lat=&quot;51.53166&quot; lon=&quot;-2.4620100000000003&quot;&gt;
    &lt;ele&gt;57.870000000000005&lt;/ele&gt;
&lt;/trkpt&gt;

This is what the output looks like:

I'll probably write something in javascript as well, and host it; that would allow the route to be displayed on a map.