Sincere answer to your question: There is evidence that it is possible to improve executive functioning in adults, some of it quite significant.
Though my understanding is definitely that 1) a lot of hyped up methods for "brain training" don't do anything, and 2) the significance of results in research varies, and 3) there's much stronger evidence for EF improvement interventions in neurodivergent and disabled people than in people who don't have an EF impairment.
Executive functioning as a personality trait is definitely not a model that there is consensus on. The brain is too complicated for us to say for sure how a lot of things work; I have always been taught that executive functioning is a skill and a series of neurocognitive processes.
Look into cognitive, neurological/neurocognitive, and developmental perspectives on executive functioning; pretty sure you'll get much more optimistic results.
This book appears to be a very thorough overview of the field, and contains both advocates and detractors of cognitive training, for a balanced perspective. From the table of contents, I would really recommend jumping straight to Part 3: Developmental Perspectives, as it sounds like the first two parts focus on a very specific range of mostly commercial brain training methods (or "methods" in some cases), whereas part 3 focuses on EF interventions in a much broader sense and specifically evaluates evidence for which types are most promising and which are least promising.
Also certain therapy modalities are specifically designed for skill-building in areas like impulsivity, decision-making, emotional regulation, and cognitive flexibility, all of which are EF skills or very dependent on EF skills. Dialectical Behavior Therapy (DBT) is probably the best field to look at for these - skill-building in those areas is its core goal.
Some DBT workbooks from an extremely credible and evidence-based publisher:
The Dialectical Behavior Therapy Skills Workbook: Practical DBT Exercises for Learning Mindfulness, Interpersonal Effectiveness, Emotion Regulation, and Distress Tolerance
The Dialectical Behavior Therapy Skills Workbook for Teens
There are also a lot of workbooks for ADHD that are sometimes more broad but also can help with executive functioning:
The Adult ADHD and Anxiety Workbook: Cognitive Behavioral Therapy Skills to Manage Stress, Find Focus, and Reclaim Your Life
The CBT Workbook for Adult ADHD: Evidence-Based Exercises to Improve Your Focus, Productivity, and Wellbeing
The Neurodivergence Skills Workbook for Autism and ADHD
The Executive Functioning Workbook for Teens
