There’s going to be times you need to leave your pet alone and the best way to reduce separation anxiety over being alone/separated/safely confined is by making it part of a daily mental+physical exercise routine.  

Pets that are comfortable by themself and that have a specific cue-tool associated with their time alone makes it very easy for them to adjust to being alone in their new home.  Instead of not knowing why they are confined/alone, they will know enrichment toys = being alone and self soothing with a focused activity.