What the evidence says
None of the sources on this page is the Abdulsalam thesis or its Table 5.3. The evidence below comes from one applied study and three methods papers on propensity score matching. It describes how covariate balance behaves after matching in general, not what that thesis table reports.
Across the applied and illustrative examples, matching decreases measured covariate imbalance. In You (2023), the standardized deviation of all covariates after matching was less than 10%. In Austin's analysis of 9104 patients with acute myocardial infarction, the largest absolute standardized difference was 0.030 in the matched sample and 0.910 in the unmatched sample. In Thoemmes's illustrative example, the largest remaining standardized difference after matching was d = .09, at the interaction between socio-economic status and problems with parents. Thoemmes's global L1 imbalance statistic fell from .938 in the unmatched sample to .919 in the matched sample. That is a small drop, and the source reads it as improved overall balance.
Formal balance tests agree with these measures. In You (2023), the p-values for covariate balance ranged from 0.453 to 0.966, so the test did not reject the hypothesis of no systematic difference. Nearest neighbour, radius and kernel matching all passed. In Thoemmes, the overall multivariate test gave χ2(8) = 13.89, p = .09, which is above the .05 threshold.
Passing these checks does not show that the propensity score model is correct. Austin's Monte Carlo simulations found that balanced covariate means do not imply a correctly specified model. Bias was greater when matching on a mis-specified score than on a correct one, even though the means were balanced. Austin reports that other diagnostics do separate the two cases. When the model was mis-specified, the variance ratio of a baseline covariate was moderately different from one. It was close to one when the model was correct. Standardized differences of interaction terms between covariates were also larger under mis-specification. Comparing the distribution of estimated propensity scores between groups was uninformative about balance and about specification.
Matching also changes the outcome estimate when confounding is present. In Thoemmes's example, the effect of moving out on neuroticism fell from d = -.41 in the unmatched sample to d = -.11 in the matched sample (t(2674) = -1.93, p = .053). This example is illustrative, not a field result.
There is no agreed cutoff for "balanced". Li (2011) states that there is no widely accepted guidance on how small a standardized difference must be. Li also argues that with matching weights, statistical tests can check balance, provided the propensity score model is correct.