Cavern Diving is the foundation for everything, if you didn’t learn the right skills in your cavern course, or didn’t master them it’s going to make the rest of the training very difficult and risk for cave diving accidents. Not many know this, but we are one who have a PADI cavern card. However my cavern course was a three day course taught in a fashion similar to the way NSSCDS teaches their courses. I moved on from there to Basic cave with an NSSCDS instructor.
I believe it depends on your skills to get cave diving certifications. A good instructor will have at least one check dive with you to see what you’ve learned and whether you have the ability to go further or not. If not, the instructor should bring you to the necessary level of skills before doing further with intro to cave.
For many instructors it’s really going to depend on what was taught during your cavern course with PADI and who taught it. Not all PADI cavern courses are created equally unfortunately. Look for an instructor that sells you training days instead of a course, cave country dive shop maybe. You might need 1 or 2 days more, so You can do the technical sidemount upgrade. I’m pretty sure you could do intro to cave with those.
Go with a technical agency for technical courses their standards have to be at a certain level, so they can retain the liab insurance, as an agency and for the individual instructors. You want good minimum standards. Most (not all) will recognize certs from other technical agencies. Sidemount was seen as an advanced level even to cave diving, requiring 100 safe cave dives to enroll (even the portions of the caves where the respective training is done require the 100 post full cave safe cave dives. So I cannot imagine a tech agency recognizing this PADI class, just like PADI cavern (at least some years back) was not accepted as a prerequisite to intro to cave diver. Giving a student the impression that recreational level ‘specialty’ classes might be equivalent in any way to technical classes is highly irregular.
But in this case I do just half. The PADI cavern specialty standards basically forbid proper cavern training. Most cave instructors are a bit wary about accepting a PADI cavern certification as equivalent to one from the established cave training agencies. This is because the bar to be a PADI cavern instructor is very low. To be an IANTD/TDI cavern instructor, You had to complete a cavern IDC, intern on 3 cavern courses and be assessed teaching a course.
The PADI cavern materials and syllabus are OK, it is just they let pretty much anyone teach it. Bottom line is that you may have to do another day on your course to make sure your skills are up to scratch. This is something that most instructors will do anyway, and will be beneficial and fun. Good luck with your training!