What would have been on the menu in an Ancient Egyptian tavern?

The underlying assumptions informing this question are not totally invalid, but present a very practical challenge. We do know pretty well what they ate, but we not know enough about what and/or how they did that in gastronomical settings, especially not for those which would relate to 'public hospitality', like eating out in a tavern. Public feasts might be another matter. And sadly, above all: No recipes.

A note on the timeframe: 6th century BCE corresponds to Late Period of ancient Egypt including the transition to 'foreign origin' rulers like the Achaemenids, thus marking perhaps the very last endpoint to be inquired about when asking of 'ancient Egypt'? The following thus concentrates on the vast timespan that came before:

Modern visitors will delight in the grilled fowl, wild or domestic, once favored by Egyptian nobles on their country estates. They will dine on Nile and Mediterranean fish prepared with little change from antiquity; praise seasoning with the zesty onions and garlic nostalgically recalled by Israelites in their escape from bondage (Numbers 11:5); and find the national vegetable in a leafy plant that may have been gathered and enjoyed by prehistoric ancestors: melukhiya.

Paradoxically, we know everything there is to know about the foodstuffs of ancient Egypt, the processes that made them ready for the kitchen, but almost nothing about cookery and gastronomy. I intend to set forth my own theory of how things were prepared and how they tasted, but this is pure hypothesis based on many characteristics of Egyptian language and art extrapolated to the realm of cuisine. […]

— Phyllis Pray Bober: "Art, Culture & Cuisine. Ancient & Medieval Gastronomy", The University Of Chicago Press: Chicago, London, 1999. gBooks

This ملخية is basically a 'mushed weed', well really just jute leaves, that looks to me quite terrible in prepared form but is said to taste really good and seems to feature a favourable nutritional and even medicinal profile.

As for the speculative recipe reconstructions, in a similar attempt that may or may be not approximate the desired outcome for this gastronomical question in a collection:

Herein is the importance of this book. Magda Mehdawy and Amr Hussein’s The Pharaoh’s Kitchen offers a collection of modern-day recipes that have evolved from pharaonic cooking techniques and ingredients. Despite the abundant depictions of food and food preparation found on pharaonic walls and reliefs, the ancient Egyptians did not leave behind any recipes, making it difficult, if not impossible, to identify the methods of food preparation and dining etiquette of their civilization.

— Magda Mehdawy & Amr Hussein: "The Pharaoh's Kitchen. Recipes from Ancient Egypt’s Enduring Food Traditions", The American University in Cairo Press: Cairo, New York, 2010. pdf on academia.edu

Again for pharaonic Egypt we slowly approach a slightly more synoptic analysis of the literary, lexicographic, iconographic and archaeological remains available for study. :

To discuss ancient Egyptian cuisine is something of a challenge. Although a rich iconographic repertoire allows any visitor to the Nile Valley today to obtain extensive information on the different cycles of agricultural production – these are represented in a very repetitive manner in the tombs of important officials from the Pharaonic period – we have no further concrete information, with rare exceptions, to give us a clearer picture of the recipes used at that time: no cuneiform tablets such as those discov- ered in Mesopotamia, which enable us to reconstruct in outline “the world’s oldest cuisine” (Bottéro, 2002); no book of Apicius to list, albeit succinctly, the ingredients of the dishes. Any attempt to discuss the Egyptian diet must therefore be based on a very heterogeneous set of sources: the medical papyri that – in the recipes of medicinal preparations – give an idea of cooking techniques in use at the time of the pharaohs; accounting records that detail products received, for example by major religious institu- tions or the royal kitchens. The many archaeological sources should of course be added to these – whether it be spoil heaps found on ancient sites, or food offerings deposited at all times in the tombs, which can sometimes allow a more direct idea of what the Egyptian diet truly entailed. […]

When combined, all these approaches allow, if not a detailed reconstruction of the menu of the Egyptians, at least a reasonable idea of what might have appeared at their tables, keeping in mind the extreme disparity that existed in this area between members of the social elite, who have left us much of the available literature, and the more modest population, who made up the majority of the country.

[…]

The foundation of the Egyptian diet was bread (te) […],
Alongside bread, beer (henqet) also played an important role in the Egyptian diet […]
Finally, a few words may be said about the other crops of ancient Egypt: what is striking, in fact, is the relatively small number of fruits and vegetables that were grown, compared with what are found today in the country. The fruits that are familiar to us are reduced, in this world, to the triad of dates, raisins, and figs; pomegranates, apples, and olives, on the other hand, seem not to have been acclimated to Egyptian soil until the New Kingdom […]

On the other hand, it should be noted that many other fruits, whose production has now become anecdotal, were essential in the diet at the time of the Pharaohs: this is the case, notably, with figs sycamore, nuts of the dôm-palm, and fruits of the persea tree . Moreover, many carbohydrate foods were available: chickpeas, lentils, lupins, bamiehs, and beans are clearly documented. Finally, the Egyptians had a wide variety of fresh vegetables: garlic, onions, leeks, celery, cabbage, radishes, lettuce, cucumbers, gourds, melons, and watermelons.

Meat was a luxury dish in Egypt: it is perhaps for this reason that scenes of slaughter are so often represented on the walls of tombs of high officials. The animals consumed regularly were often wild game […]
The problem with the kitchen scenes transmitted by the Egyptian iconographic sources arises from their subjectivity: the most prestigious animals are represented more often, as are the cooking methods that were considered most suitable in the funerary context to which most extant compositions belong […]

All available sources for Egyptian cuisine thus point to the existence of a world to which we have very limited access, where one glimpses the complexity both of certain food preparations and of the codification of table manners, of which certain texts that have survived from the wisdom literature – such as the teachings of Ptahhotep or of Kagemni – in turn give us an overview.

— Pierre Tallet: "Food in Ancient Egypt", in: John Wilkins & Robin Nadeau (eds): "A Companion to Food in the Ancient World", Wiley: Malden, Oxford, 2015.