The only type of test that food will definitely not affect in any way is the PCR test. For all other types of tests, food can be affected in one way or another. In addition to the fact that due to the food eaten in the blood, the level of glucose or, for example, the level of leukocytes may increase, the blood itself may become somewhat cloudy due to the fact that the food eaten begins to be absorbed into the blood, and since most of the analyzes are performed using photometric methods, evaluating the optical properties of the reaction mixture, the resulting turbidity of the blood can distort these indicators. In general, don't eat bagels before testing.
The question is not entirely correct. The requirements for different analyzes are different. For example, for a general clinical analysis (shows the quantitative content of various blood cells: erythrocytes, leukocytes, platelets, etc.) or before donating blood, you can eat, even need to (but the donor's diet has its own). But for the same biochemical analysis (it shows the presence of various substances in the blood: sugar, protein, etc.) it is forbidden to eat, because this can directly affect the readings, therefore the analysis will be incorrect, even because of one donut :)
Depends on what kind of analysis is planned. If you are going to donate blood, for example, for sugar, then one bagel can really spoil the picture a little and give overestimated blood sugar levels. Of course, this also depends on the donut itself. Is it sprinkled with icing sugar, is it sweet, what size it is, after all. Probably, a small unsweetened dietary bagel will not significantly affect the test result.
In a biochemical blood test, food intake can also distort the results, so you should refrain from the donut.
If we are talking about general clinical analysis (erythrocytes, leukocytes, platelets, ESR, etc.), then the bagel will most likely not affect the result. However, it is recommended to eat no later than an hour before the analysis. A dense protein meal can cause leukocytosis, which, when interpreted, can be interpreted as a sign of an inflammatory process.