This is a complex task if you have to build it, how long do you have and what facilities are available to you. You need to be positive about it, put everything else aside and just concentrate on the problem, if you have got where you are now, then you will have the aptitude to get through this.
A word of caution, you are working with dangerous voltages, so take care.
You are going to rely heavily on web based material, so I hope you have good access to the web.
You need to break the problem down into discrete sections, start with block diagrams and fill the details out as you get more information and solutions. For example, input section with emi components, bridge, transformer, output, controller, isolated feedback loop, and bridge drivers.
You will need a number of application notes to help you on your way, few of a number of examples below.
https://www.youtube.com/watch?v=jbmI3phNx-0https://article.sciencepublishinggroup.com/pdf/10.11648.j.ie.20210501.13.pdfhttps://octopart.com/blog/archives/2022/03/half-bridge-isolated-dc-dc-converter-designhttps://www.ti.com/lit/ug/sluu429b/sluu429b.pdfAn earlier reference I gave you,
https://www.poweresim.com/index2.jsp?topology...=89&deduct=190&InitNow=T&pc=94209covers the transformer, the controller section is listed as generic, you could adapt the TL494 in that role, together with the MOSFET drivers.
There is an application note here on the IR2110,
https://web.mit.edu/6.131/www/document/float_drive.pdfThe frequency setting for the TL494 is in the data sheet from TI. figure 7.1 shows the resistor and capacitor values.
Transformer, ferrite core based, this is perhaps the most complex component, and is not easy to implement without access to a selection of magnet wire, insulating materials, tape, and transformer varnish. It should also be flash tested when complete.
ttps://www.ti.com/lit/ml/slup126/slup126.pdf,
https://tahmidmc.blogspot.com/2013/02/ferrite-transformer-turns-calculation_22.htmlPerhaps the most critical part is the physical layout on a PCB, high current, fast rise time paths, and creepage and clearance becomes an issue, slots in the PCB are often needed etc.
Once built, you have to check the system for stability over the full range of input and output parameters.
To repeat, this is a complex task, provided you have the theory sorted, can understand a data sheet, follow an application note in such a way that you can adapt it for your use, and do a PCB layout, you are well on the way. Personally I have never designed a half bridge inverter, but the approach to this is no different to any other circuit design, keeping your design requirements in mind, break the problem down into easily worked sub sections, or even to the component level (transformer, for example), a then work through each section using data sheets and application notes to fill in the details.
All the best
Richard