Take a single one of your items: inventory management. There's SOOO much going on here, people look and say "What's the big deal? decrement an integer!" How do you handle payment failures and dunning management? Subscriptions? Bundles? Incomplete carts? Buy online; pick-up in store? blended inventories? multiple locations? The list goes on and the number of interconnected components makes this really hard to solve.
You're building all this, a marketplace and front ends for web & mobile? With a team of 7? I had a team of 23 and struggled to stay on top of all the nuances in just subscriptions, so you're (a) missing important use-cases or (b) way more effective than my former team. Chances are it's somewhere in between.
In turn, depending on your needs and the regulatory regimes you're working under, you may find that you could have saved time and money going with an industrial-grade solution that can seamlessly handle taxes, accounting and revenue recognition, multi-vendor logistics, credit/refunds, reverse logistics, etc. (there's a lot of etc.!), but that could be overkill for your requirements. I've seen SMBs with small digital teams build and run bespoke e-comm solutions handling all their needs (and more effectively than trying to fit a commercial square peg into a round hole), but the more complex and general their use cases, the more trouble they tend to have, especially when they get into multi-stakeholder retail scenarios (e.g., things like splitting a net-90 invoiced order between multiple future dates, vendors and warehouses, and logistics providers, while acting as a subledger that can handle revenue and income recognition properly).
Building a fully custom solution is the most expensive option today and really unnecessary. There is no reason to build your own product management system when so many flexible options exist. Just as I would never recommend building a server and push people towards containerization and the cloud, I recommend finding components that can be leveraged to streamline the custom build.
In terms of high-end headless systems, the market is large and growing. Some leading composable commerce SaaS offerings can offer free tiers and have pre-built front-ends and integrations.
At this point, the answer is always buy and then build later if necessary. Just as we once questioned building a server vs using the cloud, using pre-built flexible components gets you to market faster.
Just be careful as the market right now has many monoliths and old systems claiming to be "headless" and "composable", but in reality Magento, Salesforce, Oracle, etc. are all expensive to work with and should only be considered for basic needs.
Looking at a marketplace you can consider marketplace specific vendors like mirakl and convictional, but being niche they can be very expensive. I would instead look at composable commerce solutions that are very flexible and can meet your marketplace needs.
Right now Mirakl is the big incumbent in marketplace APIs, but whether that's the right answer will depend on your company's scale, technical capabilities, and margins.
[0] I keep a folder of examples of unmoderated third-party seller content embarrassing large companies running marketplaces, this one is my go-to example: https://www.independent.co.uk/news/world/americas/ashli-babb...