Does Draw have shapes for process engineering like Visio?
There are no builtin shapes for this, and no useable templates I have found in the likely spots.
I found an offer on G-suite Draw which looks like it matches your request. Not sure whether the objects are compatible with LO Draw, but you could check it out if you have a Google account. Selection of object shapes looks promising (I am not a process engineer, though, so you would have to make that judgement for yourself).
Downloading that to a Draw template is worth a try. Most likely you will need to copy the shapes into Draw and make that your own template.
I find the Gallery useful for keeping simple shapes. I know that some users hate it. If you have composite objects with components spread across multiple layers, it is better to keep an object collection on a separate sheet. The gallery will “flatten” composite objects, so everything is pasted back into one layer.
Note also that much of the “bells and whistles” functionality Visio provides is not available with Draw. If you need the line organizer, visual clues for crossing vs. connected lines or automated object name/function tags, you should consider buying Visio instead.
There are a few tools out there offered at no cost for personal/small business use, but I don’t know whether they contain objects suitable for process flow charts. LucidCharts and Fusion 360 - to name a couple - touch on the same range of functions, from different angles, and may be better tools for your purpose.