I was able to reproduce this on a local test site.
A key thing which you didn't mention is that it only happens if your CPT has a Views Content Template assigned to display them.
Is that true on your site?
Since Elementor added templates there is some overlap with Views templates, and it is important to use one or the other but not both when it comes to designing templates for single posts.
So before going any further, can you clarify, what are you using to create templates to design single posts of your CPT?
I'm using Elementor for only one 'single' template, and that is for the WooCommerce 'Product' CPT.
The 'Programmes', 'Sessions' and 'Testimonials' CPT's single templates are all made with Toolset.
I do have a Views shortcode in the single template for the 'Programmes' CPT (please see attached screenshot).
For single CPT's 'Sessions' and 'Testimonials' I made the templates with Toolset Fields shortcodes only, no Views.
So, there are no 'Views' assigned in the single templates for 'Sessions' and 'Testimonials'.
There are, however, Views assigned to the CPT's 'Sessions' and 'Testimonials', but to display elsewhere on the website, not on the single template.
So, the CPT's 'Sessions' and 'Testimonials' single templates contain no Elementor elements, other than the 'Elementor Library' widget in the default sidebar of the page.
Many Elementor users have switched to designing single CPT templates with Elementor instead of with Toolset Content Templates, and problems arise if you mix the two approaches, but you have confirmed that you are not.
In which case there is nothing you are doing wrong, you have identified a problem with the integration.
I need to escalate this so that it can be confirmed and then reviewed by the developers.
I'll let you know when I have some feedback to share.