Using Structure Progress, Totals and Formula Columns
Apart from the usage of generators, another source of performance load can be the use of the Progress column, the Totals columns and the Formula columns. The Jira fields by themselves used in columns have little impact as they are loaded only for the structure elements, which are currently displayed, plus a number of items below and above (to ensure smoother scrolling).
But for the progress, totals and some formulas the values will be loaded for the entire hierarchy, because such columns aggregate data across the entire hierarchy. For structures with thousands of issues this can become noticeable, but it's still much less of an impact when compared to loading the hierarchy itself.
If you have a really large instance and your structures will contain thousands of issues, a good practice is to setup a staging server with the snapshot of data, so users can try building their structures there first. In our experience, 80% of the situations, where there were some performance issues, happened while the users were experimenting with Automation and built really large and complex structures by mistake.
For more tips on building efficient structures please read the document.
Structure on Issue Page
Users can see structures on the main Structure Board accessible through the top Jira menu, on Jira dashboards, project page and also on the Issue Page. Opening a structure, built with the use of automation in any of this locations will require generation of this structure. This is pretty obvious for the main Structure Board or the Dashboard, but less intuitive for the Issue Page.
You can define, which structure will be shown on the Issue Page by default as described here: Structure Options for the Issue Page.
It's important to understand that if a really large structure is selected as the default one for some project for example, when a user opens Issue Page for an issue from this project, this large structure will be loaded. This may start affecting the performance quite significantly, so it's recommended to use smaller and simpler structures as the default ones.
You can also remove Structure widget from the Issue Page completely.
Another non-explicit structure loading will happen if you use S-JQL - an extension for JQL that allows you to run structure-based queries. Every time such a query is executed, the structure that is used in the query will be loaded. This means if you create some saved filter with S-JQL for a large structure and use it heavily somewhere, this may start affecting performance too.