Does Bayesian Theorem mean that testing of asymptopmatic people has more probability of False positives? https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_probability/bs704_probability6.html

A patient goes to see a doctor. The doctor performs a test with 99
percent reliability--that is, 99 percent of people who are sick test
positive and 99 percent of the healthy people test negative. The
doctor knows that only 1 percent of the people in the country are
sick. Now the question is: if the patient tests positive, what are the
chances the patient is sick?
The intuitive answer is 99 percent, but the correct answer is 50 percent....

Here, they consider only the reliability of the test & the prevalence of the disease in the population. Should we also consider the fact whether the patient is symptomatic or not - i.e. if the patient is asymptomatic, will it further reduce the reliability of the test?
Many people routinely test for a few lifestyle diseases once every few years as they get older - this is even if they don't exhibit any symptoms. I was wondering if this counter productive as per Bayesian probability.
 A: The point of Bayesian analysis is to take advantage of  prior information to reach a probability estimate.
If all you know are the general false positive and false negative rates and the incidence in the population then that 50% estimate is about right. If the patient is symptomatic that's more evidence that they have the disease, and increases the probability that a positive test is a true positive. You would need more data to quantify that increase.
As for

Many people routinely test for a few lifestyle diseases once every few
years as they get older - this is even if they don't exhibit any
symptoms.

whether that is worth doing is a cost benefit analysis. What is the cost of the test, in dollars which might come from the patient or be better spent elsewhere, in anxiety? What are the treatments possible if the condition is found? What are the consequences of leaving it untreated?
Bayesian analysis does not provide answers, just a framework for a part of the problem.
See Applied Probability- Bayes theorem
