Is there a system that manages project tenders?  I have seen many ERPs that have buying/shopping module, but they are focused on products and services, we subcontract to make some projects, do you have any recommendation on these cases?

I think you could check EDUCAUSE Core Data Service. Hope it might help you.

We are not using any third party solution but developing our own platform internally.

Procore is a cloud-based construction management platform that includes a tender management module. Procore allows you to create, publish, and manage tenders online, ensuring all the information is centralized in one place. By automating tender notification, evaluation, and vendor communication, the software streamlines processes and reduces time and effort.

While many ERPs have buying/shopping modules, as you mentioned, they may not cater specifically to the complexities of managing project tenders. E-Procurement Platforms or SRMs could be of help. You could also see if RFPIO fits your needs.

There are a number of titles out there.  RFPIO, Avnio, Loopio, etc.  We have tinkered, but not landed on a specific product.