Text (plain, long) automatically has line break converted to I have created a field Text(plain, long) and have a custom template
which currently only outputs this field.

{{ content.field_testing }}


When the output is rendered, all the line breaks are converted to &lt;br&gt; I need  to remove. I could add some filters but I figure there must be a way to prevent it in the first place. How can I do this?
Since you are using a custom template, the quicker way is just to use the replace() filter.

{{ content.field_testing|replace({'&lt;br&gt;': '', '&lt;br /&gt;': ''}) }}


The field formatter used in the case of a plain text field doesn't have settings, so you cannot decide if the formatter should output the &lt;br /&gt; tags you want to remove. It would probably make sense in few cases, especially if you need to replace those &lt;br /&gt; with other text, but somebody could argue that if you don't need them, you could just avoid entering new lines in the field.

The alternative would be implementing a different field formatter, but this is not as quicker as using a filter. If you just need this for this exact purpose, it sounds a bit excessive.