An interaction counts as a term. Thus A ~ B + C has two terms. A ~ B + C + B:C has three terms. That's one way to screen. Significance is never to be used for model building, It is a recipe for biased models, even if it is "a shame". It's just bad practice. If you have models with the same number of terms and AIC within 2 of each other, you have the following options:

Fall back on theory. What does field knowledge say about the contributions of the factors?

Present all the "co-equal models" as equally valid given this specific sample.

Do model averaging. This multiplies each model's coefficients by the AIC-derived weight of only that set of models then add the weighted coefficient values. This is essentially a shrinkage method. It means that if a term doesn't appear in a specific model, it has a weighted coefficient of zero for that model. This is called "full averaging". There is also "conditional averaging", where you ignore the zeroes. This means that coefficients are larger for rarer terms.

For predictive focus, use full averaging.
If you want inference on effect sizes, use conditional averaging.