There is a stage in most businesses where somebody suggests you have outgrown shared hosting. Usually it is suggested by whoever sells the next tier up.
Occasionally they are right. More often the site would run perfectly well where it is, and the upgrade buys a set of responsibilities nobody has volunteered for.
What Shared Hosting Actually Is
Your site and other sites on the same machine, with the operating system, security patching and service configuration handled for you. Resources are divided between accounts.
The reason it has a poor reputation is overselling. A server with a sensible number of accounts is quick and stable. The same hardware carrying several hundred sites is neither, and both are sold under the same name at similar prices. The model is not the problem. The density is.
What A VPS Actually Costs
The monthly fee is the small part. A VPS is a server you now own the problems of.
Security updates are yours. Firewall rules are yours. Mail configuration, PHP versions, SSL renewal, log rotation, disk monitoring, and the 4am restart when something wedges. All yours, unless you are paying for a managed plan, at which point you are back to paying someone else to do it and the price gap has closed considerably.
Plenty of small businesses move to a VPS, run it well for six months, then quietly stop patching it. An unmaintained VPS is a worse place to be than shared hosting, not a better one.
When Moving Up Genuinely Makes Sense
You need software the shared platform does not run. You have traffic or database load that a shared account cannot fairly be given. You have a compliance requirement for isolation. Or you have somebody whose actual job includes looking after it.
If none of those are true, the honest recommendation is to stay where you are and spend the difference on making the site itself better. We will tell you when we think you should move up. We are in no hurry to sell you a machine you did not need.