This is from the Italian public health centre, equivalent to PHE here and with actual analysis of causes of death:
https://www.epicentro.iss.it/coronavirus/sars-cov-2-decessi-italia#4
It is worth quoting the first 6 headings:
1. Sample
The analysis is based on a sample of 16,654 patients who died and tested positive for COVID-19 in Italy.
2. Demographics
The average age of patients who died and tested positive for COVID-19 is 78 years (median 80, range 5-100, Range InterQuartile – IQR 73-85). There are 5478 women (32.9%). Figure 1 shows that the median age of COVID-19-positive patients is over 15 years higher than that of patients who contracted the infection (median age: patients who died 80 years – patients with infection 62 years). Age data was not available for 1 patient. The figure shows the number of deaths by age group. Women who died after contracting SARS-CoV-2 infection are older than men (median age: women 83 – men 78).
3. Pre-existing pathologies
The graph presents the most common pre-existing chronic diseases (diagnosed before contracting SARS-CoV-2 infection) in deceased patients. This figure was obtained from 1453 deceased people for whom medical records could be analysed. The average number of pathologies observed in this population is 3.3 (median 3, Standard Deviation 1.9). Overall, 51 patients (3.5% of the sample) had 0 pathologies, 215 (14.8%) 1 pathology, 301 had 2 pathologies (20.7%) 886 (61.0%) had three or more pathologies. Prior to hospitalization, 25% of COVID-19 positive patients had ACE-inhibitors and 15% had therapy with Sartani (angiotensin receptor blockers). In women (n-448) the average number of diseases observed is 3.3 (median 3, Standard Deviation 1.9); in men (n-1005) the average number of pathologies observed is 3.2 (median 3, Standard Deviation 1.9). standard deviation 1.9).
4. Diagnosis of hospitalization
93.5% of hospitalisation diagnoses mention coVID-19-compatible conditions (e.g. pneumonia, respiratory failure) or symptoms (e.g. fever, breathlessness, cough). In 91 cases (6.5% of the total) the diagnosis of hospitalization was not related to the infection. In 8 cases the diagnosis of hospitalization concerned only cancer diseases, in 40 cases cardiovascular pathologies (e.g. acute myocardial infarction, heart failure, stroke), in 13 cases gastrointestinal diseases (e.g. gallbladder, intestinal perforation, intestinal occlusion, cirrhosis), in 30 other cases.
5. Symptoms
The graph shows the most commonly observed symptoms before hospitalization in COVID-19 positive patients. Breath and cough fever are the most common symptoms. Less frequent are diarrhea and emotic. 5.7% of people had no symptoms at the time of admission.
6. Complications
Respiratory failure was the most commonly observed complication in this sample (96.7% of cases), followed by acute kidney damage (23.5%), overinfection (11.0%) acute myocardial damage (9.8%).
Not that in this sample of over 16,000 deaths 96.7% died of respiratory failure and this is much harder data than the anecdotes you quote.